Multiple choice

If the length of each side of a square is increased by 10%, by what percentage does its perimeter increase?

  1. 10%

  2. 20%

  3. 11%

  4. 22%
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A Correct answer
Explanation

Perimeter P = 4s. If s increases by 10%, the new side is 1.1s. The new perimeter is 4(1.1s) = 4.4s. The increase is (4.4s - 4s) / 4s = 0.1 or 10%.

AI explanation

Since the perimeter of a square is directly proportional to its side length, any percentage change in the side length results in an identical percentage change in the perimeter. Let the initial side length be 10, making the perimeter 40, and the new side length be 11, making the new perimeter 44. The percentage increase in the perimeter is calculated as ((44 - 40) / 40) multiplied by 100, resulting in 10%.

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