Question

In a right​ triangle, the hypotenuse is 8 cm longer than the shorter leg. The longer leg measures 16 cm. Find the length of the hypotenuse.

Answer 1

20 cm

Explanation:

Let's denote the length of the shorter leg by "x". According to the problem, we know that the hypotenuse is 8 cm longer than the shorter leg, so its length is x + 8 cm. We also know that the longer leg measures 16 cm.

Using the Pythagorean theorem, we can write:

x^2 + 16^2 = (x+8)^2

Simplifying and solving for x, we get:

x^2 + 256 = x^2 + 16x + 64

Subtracting x^2 from both sides, we get:

256 = 16x + 64

Subtracting 64 from both sides, we get:

192 = 16x

Dividing both sides by 16, we get:

x = 12

Therefore, the length of the hypotenuse is x + 8 = 12 + 8 = 20 cm.