Answer:
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.