Question

The longer leg of a right triangle is 1 cm longer than the shorter leg. The hypotenuse is 9 cm longer than the shorter leg. Find the side lengths of the

triangle.
cm
Length of the shorter leg: 0
Length of the longer leg: 0
Length of the hypotenuse: 0
cm
cm

Answer 1

Shorter leg = 20 cm.

Longer leg = 21cm.

Hypotenuse = 29 cm

Explanation:

Let the shorter leg be x cm long

Then longer leg = x + 1 and hypotenuse = x + 9 cm long

So by Pythagoras:

x^2 + (x + 1)^2 = (x + 9)^2

0 = x^2 + 18x + 81 - x^2 - (x^2 + 2x + 1)

x^2 + 18x + 81 - x^2 - x^2 - 2x - 1 = 0

-x^2 + 16x + 80 = 0

x^2 - 16x - 80 = 0

(x - 20)(x + 4) = 0

So x = 20 (we ignore the negative root).

So longer leg = 20 + 1 and hypotenuse = 20 + 9.