Square — Side Increased by 25%: If the side of a square is increased by 25%, by what percent does the area increase?

Introduction / Context:Area scales with the square of a linear dimension. When a square’s side increases by a percentage, the area increases by the square of the scale factor minus 100%. This item tests quick percent-compounding intuition without algebraic complexity.

Given Data / Assumptions:

• Original side = s; new side = 1.25s
• Area formula: A = s^2; new area A' = (1.25s)^2
• Percent increase = ((A' − A)/A) * 100%

Concept / Approach:If a linear dimension scales by k, area scales by k^2. Here k = 1.25. Compute k^2 and convert to a percentage increase relative to the original area. Keep decimals exact to avoid rounding slips.

Step-by-Step Solution:

Verification / Alternative check:

Why Other Options Are Wrong:

• 125% confuses scale factor with increase.
• 50% and 53.75% underestimate the quadratic effect.
• 62.5% overestimates (mixing 1.25 and 1.5).

Common Pitfalls:

• Treating area as linear and adding 25% only once.

Final Answer:56.25%.