A rectangle is 8 m by 3 m. If the length is increased by 25% and the width is decreased by 20%, what is the new area?

A rectangle is 8 m by 3 m. If the length is increased by 25% and the width is decreased by 20%, what is the new area?

• A. 24 m^2
• B. 28 m^2
• C. 30 m^2
• D. 18 m^2

Answer: (A)

Changing the dimensions affects area by multiplying the scale factors for length and width. A 25% increase in length multiplies by 1.25, and a 20% decrease in width multiplies by 0.8. The new area equals the original area times 1.25 times 0.8. Since 1.25 × 0.8 = 1, the area stays the same as before. Compute the new dimensions: length becomes 8 × 1.25 = 10, width becomes 3 × 0.8 = 2.4. Multiply: 10 × 2.4 = 24. Therefore, the new area is 24 m^2.

Changing the dimensions affects area by multiplying the scale factors for length and width. A 25% increase in length multiplies by 1.25, and a 20% decrease in width multiplies by 0.8. The new area equals the original area times 1.25 times 0.8. Since 1.25 × 0.8 = 1, the area stays the same as before.

Compute the new dimensions: length becomes 8 × 1.25 = 10, width becomes 3 × 0.8 = 2.4. Multiply: 10 × 2.4 = 24. Therefore, the new area is 24 m^2.