Find the lengths of the sides of the rectangle if it is known that one of them is 14 cm bigger than the other, and the diagonal of the rectangle is 34 cm.

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