Hello from MrBillDoesMath!
Answer: Shorter side = 16 and longer side= 30
Discussion:
Suppose the shorter side is called "L", then the longer side is (L+14). As the diagonal of the rectangle is actually the hypotenuse of a right triangle, by Pythagoras we have:
L^2 + (L+14) ^2 = 34^2
or
L^2 + (L^2 + 28L + 14^2) = 34^2
or
2L^2 + 28L + 196 = 1156
Dividing by 2 gives
L^2 + 14L = (1156 - 196) /2 = 480
So we need to solve the quadratic:
L^2 + 14L - 480 = 0.
by the quadratic formula or factoring. In either case we find
L^2 + 14L - 480 = 0 = (L+30)*(L-16)
Taking the positive gives L = +16 ( L can't equal -30)
Regards, MrB
