Practice!

Sample Problem

If the length of a rectangle increases by 2 cm, its area will increase by 12 cm2. If the width increases by 3 cm, its area will increase by 21cm2. What is the original area of the rectangle? cm2

Solution

By increasing the length by 2 cm, we are basically adding a rectangle that is 2 cm by the width of the original rectangle. Since the area of the added rectangle is 12, the width of the original rectangle is therefore 12 ÷ 2 = 6 cm. By increasing the width by 3 cm, we are basically adding a rectangle that is 3 cm by the length of the original rectangle. Since the area of this added rectangle is 21, the length is 21 ÷ 3 = 7cm. Thus the original rectangle has an area of 7 × 6 = 42 cm2.