Question

Find the missing side lengths. Answers are in simplest radical form with the denominator rationalized.

A 45-45-90 right triangle with one of the legs labeled y, the other leg labeled 4 times the square root of 2, and the hypotenuse labeled x.

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Answer 1

missing side lengths are

leg 1 is 4√2

leg 2 is 4√2

hypotenuse is 8

Explanation:

leg 1 is y

leg 2 is 4√2

45-45-90 right triangle means

legs are equal

the longest side is the hypotenuse which is

x

pythagorean theorem =

a² + b² = c²

a and b are the legs

c is hypotenuse

(4√2)² + (4√2)² = c²

4√2 = √16*2 = √32

(√32)² + (√32)² = c²

32 + 32 = c²

64 = c²

take the square root of both sides

√64 = √c²

8 = c

c = 8