Question

Find the length of the hypotenuse of a 45°-45°-90° triangle with a leg

length of 8√8 centimeters

Answer 1

Therefore, the length of the hypotenuse of the 45°-45°-90° triangle is 32 centimeters.

Explanation:

In a 45°-45°-90° triangle, the two legs are congruent, which means that each leg is equal to the length of the hypotenuse divided by √2.

Let h be the length of the hypotenuse. Then we have:

leg = h/√2

Given that one of the legs is 8√8 centimeters, we can substitute this value into the equation above to solve for h:

8√8 = h/√2

Multiplying both sides by √2, we get:

8√8 x √2 = h

Simplifying, we get:

h = 8√16

h = 8 x 4

h = 32

Therefore, the length of the hypotenuse of the 45°-45°-90° triangle is 32 centimeters.