EXAMPLE 4 Find the length of a hypotenuse using two methods

SOLUTION

Find the length of the hypotenuse of the right triangle.

Method 1: Use a Pythagorean triple.

A common Pythagorean triple is 5, 12, 13. Notice that if you multiply the lengths of the legs of the Pythagorean triple by 2, you get the lengths of the legs of this triangle: 5 2 = 10 and 12 2 = 24. So, the length of the hypotenuse is 13 2 = 26.

EXAMPLE 4 Find the length of a hypotenuse using two methods

SOLUTION

Find the length of the hypotenuse of the right triangle.

Method 2: Use a Pythagorean triple.

x2 = 102 + 242

x2 = 100 + 576

x2 = 676

x = 26

Pythagorean Theorem

Multiply.

Add.

Find the positive square root.

GUIDED PRACTICE for Example 4

7. Find the unknown side length of the right triangle using the Pythagorean Theorem. Then use a Pythagorean triple.

x2 = 122 + 92

x2 = 144 + 81

x2 = 225

x = 15

Pythagorean Theorem

Multiply.

Add.

Find the positive square root.

SOLUTION

GUIDED PRACTICE for Example 4

A common Pythagorean triple is 6, 8, 10. Notice that if you multiply the lengths of the legs of the Pythagorean triple by 3/2, you get the lengths of the legs of the triangle: 6 3/2 = 9 and 8 3/2 = 12. So, the length of the hypotenuse is 10 3/2 = 15.

Pythagorean triple.

GUIDED PRACTICE for Example 4

8. Find the unknown side length of the right triangle using the Pythagorean Theorem. Then use a Pythagorean triple.

x2 = 482 + 142

x2 = 2304 + 196

x2 = 2500

x = 50

Pythagorean Theorem

Multiply.

Add.

Find the positive square root.

SOLUTION

GUIDED PRACTICE for Example 4

A common Pythagorean triple is 7, 24, 25. Notice that if you multiply the lengths of the legs of the Pythagorean triple by 2, you get the lengths of the legs of the triangle: 7 2 = 14 and 24 2 = 48. So, the length of the hypotenuse is 25 2 = 50.

Pythagorean triple.