Question

The area and perimeter of a rectangle are numerically equal. If the length is three units longer than the width, find the width.

5 units

2 units

3 units

4 units

Answer 1

Let width = w. Then length = w + 3, and area = perimeter gives
w(w+3) = 2(w + w+3) = 4w + 6.
So w^2 + 3w = 4w + 6 → w^2 − w − 6 = 0 → (w−3)(w+2)=0.
Width = 3 units (positive root).