Equal areas – Square vs rectangle with offset sides: A square and a rectangle have equal area. The rectangle’s length is 5 cm more than the square’s side; its breadth is 3 cm less than the square’s side. Find the rectangle’s perimeter.

Introduction / Context:Let the square side be x. The rectangle’s dimensions become (x + 5) and (x − 3). Equal areas give an equation to solve for x, and hence perimeter.

Given Data / Assumptions:

• Square side = x cm.
• Rectangle: length = x + 5; breadth = x − 3.

Concept / Approach:Set x^2 = (x + 5)(x − 3) and solve for x; compute perimeter P = 2[(x + 5) + (x − 3)].

Step-by-Step Solution:

Verification / Alternative check:Area check: square 7.5^2 = 56.25; rectangle 12.5 * 4.5 = 56.25 ✔️

Why Other Options Are Wrong:15, 18, 26 come from miscomputing x or forgetting to double for perimeter.

Common Pitfalls:Sign errors when expanding (x + 5)(x − 3); arithmetic errors with decimals.

Final Answer:34 cm