If a rectangle has length 8 and width 3, and you increase width by 2% and length by 5%, what is approximate percentage increase in area?

• A. About 5%
• B. About 10%
• C. About 7.1%
• D. About 3%

Answer: (C)

When you increase each dimension, the area scales by the product of those two growth factors. A 5% increase in length multiplies the length by 1.05, and a 2% increase in width multiplies the width by 1.02. So the new area is the original area times 1.05 × 1.02.

Calculate the product: 1.05 × 1.02 = 1.071. This means the area grows by 7.1%. If you check with the actual numbers, the original area is 8 × 3 = 24. The new dimensions give an area of 8.4 × 3.06 = 25.704, which is 24 × 1.071 = 25.704, a 1.704 increase, i.e., 7.1% of 24.