45/45/90 Right Isosceles Triangles - Math
Card 0 of 48
An isosceles triangle has a base of 6 and a height of 4. What is the perimeter of the triangle?
An isosceles triangle has a base of 6 and a height of 4. What is the perimeter of the triangle?
An isosceles triangle is basically two right triangles stuck together. The isosceles triangle has a base of 6, which means that from the midpoint of the base to one of the angles, the length is 3. Now, you have a right triangle with a base of 3 and a height of 4. The hypotenuse of this right triangle, which is one of the two congruent sides of the isosceles triangle, is 5 units long (according to the Pythagorean Theorem).
The total perimeter will be the length of the base (6) plus the length of the hypotenuse of each right triangle (5).
5 + 5 + 6 = 16
An isosceles triangle is basically two right triangles stuck together. The isosceles triangle has a base of 6, which means that from the midpoint of the base to one of the angles, the length is 3. Now, you have a right triangle with a base of 3 and a height of 4. The hypotenuse of this right triangle, which is one of the two congruent sides of the isosceles triangle, is 5 units long (according to the Pythagorean Theorem).
The total perimeter will be the length of the base (6) plus the length of the hypotenuse of each right triangle (5).
5 + 5 + 6 = 16
Compare your answer with the correct one above
The base of a right isosceles triangle is 8 inches. The hypotenuse is not the base. What is the area of the triangle in inches?
The base of a right isosceles triangle is 8 inches. The hypotenuse is not the base. What is the area of the triangle in inches?
To find the area of a triangle, multiply the base by the height, then divide by 2. Since the short legs of an isosceles triangle are the same length, we need to know only one to know the other. Since, a short side serves as the base of the triangle, the other short side tells us the height.
To find the area of a triangle, multiply the base by the height, then divide by 2. Since the short legs of an isosceles triangle are the same length, we need to know only one to know the other. Since, a short side serves as the base of the triangle, the other short side tells us the height.
Compare your answer with the correct one above
An isosceles right triangle has a hypotenuse of 
. Find its area.
An isosceles right triangle has a hypotenuse of
In order to calculate the triangle's area, we need to find the lengths of its legs. An isosceles triangle is a special triangle due to the values of its angles. These triangles are referred to as 
triangles and their side lengths follow a specific pattern that states that one can calculate the length of the legs of an isoceles triangle by dividing the length of the hypotenuse by the square root of 2.
Now we can calculate the area using the formula
Now, convert to feet.
In order to calculate the triangle's area, we need to find the lengths of its legs. An isosceles triangle is a special triangle due to the values of its angles. These triangles are referred to as
Now we can calculate the area using the formula
Now, convert to feet.
Compare your answer with the correct one above
In an isosceles right triangle, two sides equal 
. Find the length of side 
.
In an isosceles right triangle, two sides equal
This problem represents the definition of the side lengths of an isosceles right triangle. By definition the sides equal 
, 
, and 
. However, if you did not remember this definition one can also find the length of the side using the Pythagorean theorem 
.
This problem represents the definition of the side lengths of an isosceles right triangle. By definition the sides equal
Compare your answer with the correct one above
ABCD is a square whose side is 
units. Find the length of diagonal AC.
ABCD is a square whose side is
To find the length of the diagonal, given two sides of the square, we can create two equal triangles from the square. The diagonal line splits the right angles of the square in half, creating two triangles with the angles of 
, 
, and 
degrees. This type of triangle is a special right triangle, with the relationship between the side opposite the 
degree angles serving as x, and the side opposite the 
degree angle serving as 
.
Appyling this, if we plug 
in for 
we get that the side opposite the right angle (aka the diagonal) is 
To find the length of the diagonal, given two sides of the square, we can create two equal triangles from the square. The diagonal line splits the right angles of the square in half, creating two triangles with the angles of
Appyling this, if we plug
Compare your answer with the correct one above
The area of a square is 
. Find the length of the diagonal of the square.
The area of a square is
If the area of the square is 
, we know that each side of the square is 
, because the area of a square is 
.
Then, the diagonal creates two 
special right triangles. Knowing that the sides = 
, we can find that the hypotenuse (aka diagonal) is 
If the area of the square is
Then, the diagonal creates two
Compare your answer with the correct one above
What is the area of a square that has a diagonal whose endpoints in the coordinate plane are located at (-8, 6) and (2, -4)?
What is the area of a square that has a diagonal whose endpoints in the coordinate plane are located at (-8, 6) and (2, -4)?
Compare your answer with the correct one above
An isosceles triangle has a hypotenuse of 
. Find the length of its sides, 
.
An isosceles triangle has a hypotenuse of
An isosceles triangle is a special triangle due to the values of its angles. These triangles are referred to as 
triangles and their side lengths follow a specific pattern that states you can calculate the length of the legs of an isoceles triangle by dividing the length of the hypotenuse by the square root of 2
An isosceles triangle is a special triangle due to the values of its angles. These triangles are referred to as
Compare your answer with the correct one above
The measure of the sides of this isosceles right triangle are 
. Find the measure of its hypotenuse, 
.
The measure of the sides of this isosceles right triangle are
An isosceles triangle is a special triangle due to the values of its angles. These triangles are referred to as 
triangles and their side lenghts follow a specific pattern that states you can calculate the length of the hypotenuse of an isoceles triangle by multiplying the length of one of the legs by the square root of 2.
An isosceles triangle is a special triangle due to the values of its angles. These triangles are referred to as
Compare your answer with the correct one above
The hypotenuse of an isosceles right triangle has a measure of 
. Find its perimeter.
The hypotenuse of an isosceles right triangle has a measure of
In order to calculate the triangle's perimeter, we need to find the lengths of its legs. An isosceles triangle is a special triangle due to the values of its angles. These triangles are referred to as 
triangles and their side lengths follow a specific pattern that states that one can calculate the length of the legs of an isoceles triangle by dividing the length of the hypotenuse by the square root of 2.
Now we can calculate the perimeter by doubling 
and adding 
.
In order to calculate the triangle's perimeter, we need to find the lengths of its legs. An isosceles triangle is a special triangle due to the values of its angles. These triangles are referred to as
Now we can calculate the perimeter by doubling
Compare your answer with the correct one above
The side lengths of an isoceles right triangle measure 
. Find its perimeter.
The side lengths of an isoceles right triangle measure
An isosceles triangle is a special triangle due to the values of its angles. These triangles are referred to as 
triangles and their side lenghts follow a specific pattern that states you can calculate the length of the hypotenuse of an isoceles triangle by multiplying the length of one of the legs by the square root of 2.
Now we can calculate the perimeter by doubling 
and adding 
.
An isosceles triangle is a special triangle due to the values of its angles. These triangles are referred to as
Now we can calculate the perimeter by doubling
Compare your answer with the correct one above
A triangle has two angles equal to 
and two sides equal to 
. What is the perimeter of this triangle?
A triangle has two angles equal to
When a triangle has two angles equal to 
, it must be a 
isosceles right triangle.
The pattern for the sides of a 
is 
.
Since two sides are equal to 
, this triangle will have sides of 
.
Add them all together to get 
.
When a triangle has two angles equal to
The pattern for the sides of a
Since two sides are equal to
Add them all together to get
Compare your answer with the correct one above
The base of a right isosceles triangle is 8 inches. The hypotenuse is not the base. What is the area of the triangle in inches?
The base of a right isosceles triangle is 8 inches. The hypotenuse is not the base. What is the area of the triangle in inches?
To find the area of a triangle, multiply the base by the height, then divide by 2. Since the short legs of an isosceles triangle are the same length, we need to know only one to know the other. Since, a short side serves as the base of the triangle, the other short side tells us the height.
To find the area of a triangle, multiply the base by the height, then divide by 2. Since the short legs of an isosceles triangle are the same length, we need to know only one to know the other. Since, a short side serves as the base of the triangle, the other short side tells us the height.
Compare your answer with the correct one above
An isosceles right triangle has a hypotenuse of . Find its area.
An isosceles right triangle has a hypotenuse of
In order to calculate the triangle's area, we need to find the lengths of its legs. An isosceles triangle is a special triangle due to the values of its angles. These triangles are referred to as triangles and their side lengths follow a specific pattern that states that one can calculate the length of the legs of an isoceles triangle by dividing the length of the hypotenuse by the square root of 2.
Now we can calculate the area using the formula
Now, convert to feet.
In order to calculate the triangle's area, we need to find the lengths of its legs. An isosceles triangle is a special triangle due to the values of its angles. These triangles are referred to as
Now we can calculate the area using the formula
Now, convert to feet.
Compare your answer with the correct one above
In an isosceles right triangle, two sides equal . Find the length of side .
In an isosceles right triangle, two sides equal
This problem represents the definition of the side lengths of an isosceles right triangle. By definition the sides equal , , and . However, if you did not remember this definition one can also find the length of the side using the Pythagorean theorem .
This problem represents the definition of the side lengths of an isosceles right triangle. By definition the sides equal
Compare your answer with the correct one above
ABCD is a square whose side is units. Find the length of diagonal AC.
ABCD is a square whose side is
To find the length of the diagonal, given two sides of the square, we can create two equal triangles from the square. The diagonal line splits the right angles of the square in half, creating two triangles with the angles of , , and degrees. This type of triangle is a special right triangle, with the relationship between the side opposite the degree angles serving as x, and the side opposite the degree angle serving as .
Appyling this, if we plug in for we get that the side opposite the right angle (aka the diagonal) is
To find the length of the diagonal, given two sides of the square, we can create two equal triangles from the square. The diagonal line splits the right angles of the square in half, creating two triangles with the angles of
Appyling this, if we plug
Compare your answer with the correct one above
The area of a square is . Find the length of the diagonal of the square.
The area of a square is
If the area of the square is , we know that each side of the square is , because the area of a square is .
Then, the diagonal creates two special right triangles. Knowing that the sides = , we can find that the hypotenuse (aka diagonal) is
If the area of the square is
Then, the diagonal creates two
Compare your answer with the correct one above
What is the area of a square that has a diagonal whose endpoints in the coordinate plane are located at (-8, 6) and (2, -4)?
What is the area of a square that has a diagonal whose endpoints in the coordinate plane are located at (-8, 6) and (2, -4)?
Compare your answer with the correct one above
An isosceles triangle has a hypotenuse of . Find the length of its sides, .
An isosceles triangle has a hypotenuse of
An isosceles triangle is a special triangle due to the values of its angles. These triangles are referred to as triangles and their side lengths follow a specific pattern that states you can calculate the length of the legs of an isoceles triangle by dividing the length of the hypotenuse by the square root of 2
An isosceles triangle is a special triangle due to the values of its angles. These triangles are referred to as
Compare your answer with the correct one above
The measure of the sides of this isosceles right triangle are . Find the measure of its hypotenuse, .
The measure of the sides of this isosceles right triangle are
An isosceles triangle is a special triangle due to the values of its angles. These triangles are referred to as triangles and their side lenghts follow a specific pattern that states you can calculate the length of the hypotenuse of an isoceles triangle by multiplying the length of one of the legs by the square root of 2.
An isosceles triangle is a special triangle due to the values of its angles. These triangles are referred to as
Compare your answer with the correct one above