Problem 2 · Compare linear and quadratic scaling · 3 points
Made by AI and not reviewed by a real person.
A square is enlarged so that its area’s percent increase is 24 percentage points greater than its perimeter’s percent increase. By what percent did each side increase?
- 20%
- 40%
- 12%
- 24%
- 44%
Show a hint
- Imagine multiplying every side by the same unknown factor. How would the perimeter and area respond?
- Let t be the fractional increase in side length. Express both percent increases in terms of t, then compare them.
Show the answer and solution
Answer: A — 20%
Let t be the fractional increase in each side. The perimeter increases by 100t%, while the area increases by 100((1+t)² − 1)%. Their difference gives t² + t = 0.24, or (t − 0.2)(t + 1.2) = 0. Since the side increased, t = 0.2, so the answer is 20%. The 44% choice is the area’s increase, not the side’s.