# SSAT Upper Level Math : Properties of Triangles

## Example Questions

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### Example Question #1 : 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.

Explanation:

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 : How To Find The Perimeter Of A Right Triangle

Which of these polygons has the same perimeter as a right triangle with legs 6 feet and 8 feet?

A regular pentagon with sidelength one yard.

A regular hexagon with sidelength one yard.

A regular decagon with sidelength one yard.

A regular octagon with sidelength one yard.

None of the other responses is correct.

A regular octagon with sidelength one yard.

Explanation:

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 #2 : How To Find The Perimeter Of A Right Triangle

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

Explanation:

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.

Explanation:

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?

Explanation:

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

Explanation:

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

Explanation:

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?

Explanation:

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 #10 : Understand Categories And Subcategories Of Two Dimensional Figures: Ccss.Math.Content.5.G.B.3

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.

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.

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.

Explanation:

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 #1 : How To Find The Length Of The Side Of A Right Triangle

A right triangle has a hypotenuse of 39 and one leg is 36. What is the length of the other leg?