All SSAT Upper Level Math Resources
Example Questions
Example Question #3 : Perimeter Of A Triangle
What is the perimeter of a right triangle with hypotenuse
and a leg of length ?It cannot be determined from the information given.
Using the Pythagorean Theorem, the length of the second leg can be determined.
We are given the length of the hypotenuse and one leg.
The perimeter of the triangle is the sum of the lengths of the sides.
Example Question #1 : Properties Of Triangles
Which of these polygons has the same perimeter as a right triangle with legs 6 feet and 8 feet?
A regular decagon with sidelength one yard.
A regular hexagon with sidelength one yard.
A regular pentagon with sidelength one yard.
None of the other responses is correct.
A regular octagon with sidelength one yard.
A regular octagon with sidelength one yard.
A right triangle with legs 6 feet and 8 feet has hypotentuse 10 feet, as this is a right triangle that confirms to the well-known Pythagorean triple 6-8-10. The perimeter is therefore
feet, or 8 yards.We are looking for a polygon with this perimeter. Each choice is a polygon with all sides one yard long, so we want the polygon with eight sides - the regular octagon is the correct choice.
Example Question #442 : Geometry
The lengths of the legs of a right triangle are
units and units. What is the perimeter of this right triangle?units
units
units
units
units
First, we need to use the Pythagorean Theorem to find the hypotenuse of the triangle.
Now, add up all three side lengths to find the perimeter of the triangle.
Example Question #3 : How To Find The Perimeter Of A Right Triangle
A right triangle has leg lengths of
and . Find the perimeter of this triangle.
First, use the Pythagorean Theorem to find the length of the hypotenuse.
Substituting in
and for and (the lengths of the triangle's legs), we get:
Now, add up the three sides to find the perimeter:
Example Question #4 : How To Find The Perimeter Of A Right Triangle
What is the perimeter of a right triangle with legs of length
and , respectively?
In order to find the perimeter
of the right triangle, we need to first find the missing length of the hypotenuse. In order to find the hypotenuse, use the Pythagorean Theorem:, where and are the lengths of the legs of the triangle, and is the length of the hypotenuse.
Substituting in our known values:
Now that we have the lengths of all sides of the right triangle, we can calculate the perimeter:
Example Question #5 : How To Find The Perimeter Of A Right Triangle
What is the perimeter of a right triangle with a hypotenuse of length
and a leg of length ?
Not enough information provided
In order to find the perimeter
of the right triangle, we need to first find the missing length of the second leg. In order to find the second leg, use the Pythagorean Theorem:, where and are the lengths of the legs of the triangle, and is the length of the hypotenuse.
Substituting in our known values:
Subtracting
from each side of the equation lets us isolate the variable for which we are solving:
Now that we have the lengths of all three sides of the right triangle, we can calculate the perimeter
:
Example Question #6 : How To Find The Perimeter Of A Right Triangle
Find the perimeter
of a right triangle with two legs of length and , respectively.
Not enough information provided
In order to find the perimeter
of the right triangle, we need to first find the missing length of the hypotenuse. In order to find the length of the hypotenuse, use the Pythagorean Theorem:, where and are the lengths of the legs of the triangle, and is the length of the hypotenuse.
Substituting in our known values:
Now that we have all three sides of the right triangle, we can calculate the perimeter:
Example Question #1 : Right Triangles
If a
right triangle is similar to a right triangle, which of the other triangles must also be a similar triangle?
For the triangles to be similar, the dimensions of all sides must have the same ratio by dividing the 3-4-5 triangle.
The 6-8-10 triangle will have a scale factor of 2 since all dimensions are doubled the original 3-4-5 triangle.
The only correct answer that will yield similar ratios is the
triangle with a scale factor of 4 from the 3-4-5 triangle.The other answers will yield different ratios.
Example Question #2 : Right Triangles
What is the main difference between a right triangle and an isosceles triangle?
A right triangle has to have a
angle and an isosceles triangle has to have equal, base angles.A right triangle has to have a
angle and an isosceles triangle has to have equal, base angles.A right triangle has to have a
angle and an isosceles triangle has to have equal, base angles.A right triangle has to have a
angle and an isosceles triangle has to have equal, base angles.An isosceles triangle has to have a
angle and a right triangle has to have equal, base angles.A right triangle has to have a
angle and an isosceles triangle has to have equal, base angles.By definition, a right triangle has to have one right angle, or a
angle, and an isosceles triangle has equal base angles and two equal side lengths.Example Question #3 : Properties Of Triangles
A right triangle has a hypotenuse of 39 and one leg is 36. What is the length of the other leg?
You may recognize these numbers as multiples of 13 and 12 (each by a factor of 3) and remember that sides of length 5, 12 and 13 make a special right triangle. So the other leg would be 15
.If you don't remember this, you can use Pythagorean theorem:
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