You are given the area of the rectangle which is 100 ft^2.
We know that the area of a rectangle is given by length x width.
It is also given that L = W + 15 (because you want the rectangle to be longer)
So substituting the values, we have:
W(W+15) = 100
W² + 15W - 100 = 0
(W+20) (W-5) = 0
W = -20; W = 5
(-20 is an extraneous solution)
Solving for L:
L = 5 + 15 = 20
The dimensions of the rectangle is 20 ft by 5 ft.
