the boat launch shown is 32 meters longer than the rise of the ramp. The run is 31 meters longer than the rise. How long are the three sides of the ramp?

Answer 1

rise --- x m
hypotenuse -- x+32
run --- x+31

x^2 + (x+31)^2 = (x+32)^2
x^2 + x^2 + 62x + 961 = x^2 + 64x + 1024
x^2 - 2x - 63 = 0
(x-9)(x+7) = 0
x = 9, or x = -7 which would be silly

the sides are 9, 40, and 41

check:
9^2 + 40^2 = 41^2, true!