Find the dimensions of the original rectangle.

Question

A rectangle is 15 feet longer than it is wide. If its length and width are decreased by 5 feet, its area is decreased by 200 square feet.

Answer 1

This is a typical Algebra problem inside Geometry. 

We know A = LW.

A₁ = (W+15)W = W²+15W (This is the length 15 more than width)

A₂ = (W+15-5)(W-5) = (W+10)(W-5) = W² + 5W - 50 (This is decreasing A₁ length and width by 5 each)

And if A₂ is decreasing the original area by 200, we get:

(W² + 15W) - 200 = W² + 5W - 50

which gives us:

10W = 150

so, W = 15

The original is A₁ = 30x15 = LxW = 450

New is A₂ = 25x10 = 250, which is 200 less than original