Triangles - SSAT Middle Level Quantitative
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An equilateral triangle has perimeter 8 feet 6 inches. How long is one side?
An equilateral triangle has perimeter 8 feet 6 inches. How long is one side?
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One foot is equal to 12 inches, so the perimeter 8 feet 6 inches is equal to 
inches.
An equilateral triangle has three sides of equal measure, so divide its perimeter by 3:
To convert 34 inches to feet and inches:
One side measures 2 feet 10 inches.
One foot is equal to 12 inches, so the perimeter 8 feet 6 inches is equal to
An equilateral triangle has three sides of equal measure, so divide its perimeter by 3:
To convert 34 inches to feet and inches:
One side measures 2 feet 10 inches.
A triangle has sides 
feet, 
feet, and 
feet. Calculate its perimeter.
A triangle has sides
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The perimeter of any figure is the sum of the lengths of the sides: 
.
The perimeter of any figure is the sum of the lengths of the sides:
Which of these choices can the perimeter of an isosceles triangle possibly be if you know that two sides have lengths 12 and 13?
Which of these choices can the perimeter of an isosceles triangle possibly be if you know that two sides have lengths 12 and 13?
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An isosceles triangle has two sides of equal length. If two sides of an isoscelese triangle are of length 12 and 13, then the third must be of length 12 or 13.
This makes the perimeter either
or
Of our choices, we choose 38.
An isosceles triangle has two sides of equal length. If two sides of an isoscelese triangle are of length 12 and 13, then the third must be of length 12 or 13.
This makes the perimeter either
or
Of our choices, we choose 38.
The perimeter of an isosceles triangle is 18. What is a possible list of the lengths of the sides?
The perimeter of an isosceles triangle is 18. What is a possible list of the lengths of the sides?
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Since it is isosceles, 2 of the sides must be equal. They must also add to 18.
Since it is isosceles, 2 of the sides must be equal. They must also add to 18.
An equilateral triangle has perimeter 
centimeters. How long is one side?
An equilateral triangle has perimeter
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An equilateral triangle has three sides of equal measure, so divide its perimeter by 
:
An equilateral triangle has three sides of equal measure, so divide its perimeter by
A right triangle with hypotenuse 65 has one leg of length 60. What is its perimeter?
A right triangle with hypotenuse 65 has one leg of length 60. What is its perimeter?
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By the Pythagorean Theorem, if 
and 
are the legs of a right triangle and 
is its hypotenuse, then
.
Set 
and solve for 
:
The perimeter of the triangle - the sum of the sidelengths - is
.
By the Pythagorean Theorem, if
Set
The perimeter of the triangle - the sum of the sidelengths - is
Find the perimeter of the triangle above.
Note: Figure not drawn to scale.
Find the perimeter of the triangle above.
Note: Figure not drawn to scale.
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The perimeter of a shape is the length around the shape. In order to find the perimeter of a triangle, add the lengths of the sides: 
.
Because the lengths are in inches, the answer must be in inches as well.
The perimeter of a shape is the length around the shape. In order to find the perimeter of a triangle, add the lengths of the sides:
Because the lengths are in inches, the answer must be in inches as well.
What is the perimeter of an equilateral triangle with a side length 
?
What is the perimeter of an equilateral triangle with a side length
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The perimeter is equal to the sum of the length of the sides. An equilateral triangle has three sides with equal lengths.
The perimeter is equal to the sum of the length of the sides. An equilateral triangle has three sides with equal lengths.
A right triangle has legs 
feet and 
feet long. What is its perimeter, in inches?
A right triangle has legs
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The length of the hypotenuse of the triangle can be found using the Pythagorean Theorem. Substitute 
:
feet
Its perimeter is 
feet. Multiply by 12 to get the perimeter in inches:
inches
The length of the hypotenuse of the triangle can be found using the Pythagorean Theorem. Substitute
Its perimeter is
If the triangle below is an isosceles triangle, what of the following choices could be its perimeter?
If the triangle below is an isosceles triangle, what of the following choices could be its perimeter?
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An isosceles triangle has 2 equal sides and a third side that is unequal. If one given side is 5 and the other is 7, then the third missing side must equal either 5 or 7. If the missing side has length 5, then the perimeter is 17 (5+5+7). If the missing side is of length 7, then the perimeter is 19 (7+7+5). Of the two, only 19 is an answer choice, so the correct answer is 19.
An isosceles triangle has 2 equal sides and a third side that is unequal. If one given side is 5 and the other is 7, then the third missing side must equal either 5 or 7. If the missing side has length 5, then the perimeter is 17 (5+5+7). If the missing side is of length 7, then the perimeter is 19 (7+7+5). Of the two, only 19 is an answer choice, so the correct answer is 19.
The perimeter of equilateral triangle QRS is 4 times the perimeter of equilateral triangle TUV. If the perimeter of QRS is 36, what is the length of one side of TUV?
The perimeter of equilateral triangle QRS is 4 times the perimeter of equilateral triangle TUV. If the perimeter of QRS is 36, what is the length of one side of TUV?
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If the perimeter of QRS is 4 times the perimeter of TUV, and the perimeter of QRS is 36, then the perimeter of TUV is equal to 36 divided by 4, which is 9. If the perimeter of equilateral triangle TUV is 9, then each individual side must have length 3.
If the perimeter of QRS is 4 times the perimeter of TUV, and the perimeter of QRS is 36, then the perimeter of TUV is equal to 36 divided by 4, which is 9. If the perimeter of equilateral triangle TUV is 9, then each individual side must have length 3.
Find the perimeter of a triangle with sides 
, 
, and 
.
Find the perimeter of a triangle with sides
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Perimeter involves adding up all of the sides of the shapes; in this case, it's a triangle. Perimeter equals 
. Therefore, the answer is 
.
Perimeter involves adding up all of the sides of the shapes; in this case, it's a triangle. Perimeter equals
What is the perimeter, in feet, of an equilateral triangle that has a side of 36 inches?
What is the perimeter, in feet, of an equilateral triangle that has a side of 36 inches?
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Given that there are 12 inches in a foot, 36 inches is equal to 3 feet because 36 divided by 12 equals 3.
In an equilateral triangle, each side is equal. Thus, if one side is 3 feet long, that means that each of the other two sides are also 3 feet long.
Add the sides together to find the total perimeter.
The perimeter of the triangle is 9 feet.
Given that there are 12 inches in a foot, 36 inches is equal to 3 feet because 36 divided by 12 equals 3.
In an equilateral triangle, each side is equal. Thus, if one side is 3 feet long, that means that each of the other two sides are also 3 feet long.
Add the sides together to find the total perimeter.
The perimeter of the triangle is 9 feet.
The perimeter of an isosceles triangle is 19. What is the possible list of the lengths of the sides?
The perimeter of an isosceles triangle is 19. What is the possible list of the lengths of the sides?
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Since the triangle is an isoscles, two of the sides must be equal. They must also add to 
. Looking at the possibilities, only 
have two sides that are the same length. Now we need to check the triangle inequality to make sure the lengths create a triangle. The triangle inequality is:
Plugging 
into these inequalities we get:
Therefore, the inequalities hold true thus, 
creates a triangle. Now we need to look at the sum of the lengths:
Therefore, 
is the correct answer.
Since the triangle is an isoscles, two of the sides must be equal. They must also add to
Plugging
Therefore, the inequalities hold true thus,
Therefore,
Find the perimeter of an equilateral triangle with a base of 11in.
Find the perimeter of an equilateral triangle with a base of 11in.
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To find the perimeter of a triangle, we will use the following formula:
where a, b, and c are the lengths of the sides of the triangle.
Now, we know the base of the equilateral triangle is 11in. Because it is an equilateral triangle, all sides are equal. Therefore, all sides are 11in.
So, we can substitute. We get
To find the perimeter of a triangle, we will use the following formula:
where a, b, and c are the lengths of the sides of the triangle.
Now, we know the base of the equilateral triangle is 11in. Because it is an equilateral triangle, all sides are equal. Therefore, all sides are 11in.
So, we can substitute. We get
What is the area of a triangle with a base of 
and a height of 
?
What is the area of a triangle with a base of
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The formula for the area of a triangle is Area=\frac{1}{2}$times basetimes height.
Plug the given values into the formula to solve:
Area=\frac{1}{2}$times 12times 3
Area=\frac{1}{2}$times 36
Area=18
The formula for the area of a triangle is Area=\frac{1}{2}$times basetimes height.
Plug the given values into the formula to solve:
Area=\frac{1}{2}$times 12times 3
Area=\frac{1}{2}$times 36
Area=18
A right triangle has legs 90 centimeters and 16 centimeters, What is its area?
A right triangle has legs 90 centimeters and 16 centimeters, What is its area?
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The legs of a right triangle are its base and height, so use the area formula for a triangle with these dimension. Setting 
:
The legs of a right triangle are its base and height, so use the area formula for a triangle with these dimension. Setting
A triangle has base 18 inches and height 14 inches. What is its area?
A triangle has base 18 inches and height 14 inches. What is its area?
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Use the area formula for a triangle, setting 
:
Use the area formula for a triangle, setting
What is the area of the above triangle?
What is the area of the above triangle?
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The two legs of a right triangle can serve as its base and its height. The area of the triangle is half the product of the two:
That is, the area is 84 square inches.
The two legs of a right triangle can serve as its base and its height. The area of the triangle is half the product of the two:
That is, the area is 84 square inches.
What is the area of the above triangle?
What is the area of the above triangle?
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The two legs of a right triangle can serve as its base and its height. The area of the triangle is half the product of the two:
That is, the area is 3,000 square millimeters.
The two legs of a right triangle can serve as its base and its height. The area of the triangle is half the product of the two:
That is, the area is 3,000 square millimeters.