A carpebter is making a brace in the shape of a right triangle. The hyp. is 41 inches long. The longer leg will be 31 inches longer than the shorter leg. Write a quadriatic equation that models the situation.

Answer 1

just plug in the numbers.

s^2 + (s+31)^2 = 41^2

to solve it, keep going:
s^2 + s^2 + 62s + 961 = 1681
2s^2 + 62s - 720 = 0
s^2 + 31s - 360 = 0
(s-9)(s+41) = 0
s = 9

the legs are 9 and 40