How to find the length of the hypotenuse of a right triangle : Pythagorean Theorem

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SSAT Upper Level Quantitative › How to find the length of the hypotenuse of a right triangle : Pythagorean Theorem

Questions 1 - 6
1

A right triangle has legs with the lengths and . Find the length of the hypotenuse.

Explanation

Use the Pythagorean Theorem to find the length of the hypotenuse.

2

Parallelogram2

Give the perimeter of the above parallelogram if .

Explanation

By the Theorem:

, and

The perimeter of the parallelogram is

3

Find the length of the hypotenuse in the right triangle below.

12

Explanation

Use the Pythagorean Theorem to find the hypotenuse.

4

The base and height of a right triangle are each 1 inch. What is the hypotenuse?

Explanation

You need to use the Pythagorean Theorem, which is .

Add the first two values and you get . Take the square root of both sides and you get .

5

If James traveled north and John traveled west from the same town, how many miles away will they be from each other when they reach their destinations?

Explanation

The distances when put together create a right triangle.

The distance between them will be the hypotenuse or the diagonal side.

You use Pythagorean Theorem or to find the length.

So you plug and for and which gives you,

or .

Then you find the square root of each side and that gives you your answer of .

6

A right triangle has legs with lengths of units and units. What is the length of the hypotenuse?

units

units

units

units

Explanation

Using the numbers given to us by the question,

units

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