Squares – area ratio to perimeter ratio: Given two squares whose areas are in the ratio 225 : 256, find the ratio of their perimeters.

Introduction / Context:For similar figures like squares, side lengths scale with the square root of area scale. Perimeter is linear in side length.

Given Data / Assumptions:

• Area ratio A₁:A₂ = 225:256.

Concept / Approach:Side ratio = √(area ratio) = 15:16. Perimeter ratio equals side ratio.

Step-by-Step Solution:

Verification / Alternative check:Pick side lengths 15 and 16; perimeters are 60 and 64 ⇒ 15:16.

Why Other Options Are Wrong:25:16 confuses area with perimeter; 16:15 inverts; 17:16 is unrelated.

Common Pitfalls:Forgetting that perimeter is linear, not quadratic.

Final Answer:15:16.