Equal areas – Square vs rectangle (square side 40 cm, rectangle length 64 cm):\nA square has side 40 cm. A rectangle has the same area and length 64 cm. Find the perimeter of the rectangle.

Introduction / Context:
Equal areas let us find the unknown breadth of the rectangle, after which perimeter is straightforward.

Given Data / Assumptions:

• Square side = 40 cm ⇒ area = 40 * 40 = 1600 sq cm.
• Rectangle length = 64 cm; breadth unknown.

Concept / Approach:
Set rectangle area = 1600 = 64 * breadth ⇒ breadth, then compute perimeter 2(L + B).

Step-by-Step Solution:

Verification / Alternative check:
Area check: 64 * 25 = 1600 equals square area ✔️

Why Other Options Are Wrong:
187, 149, 194 arise from arithmetic slips or using 64 + 25 without doubling.

Common Pitfalls:
Forgetting perimeter doubles the sum of sides; mixing up area and perimeter formulas.

Final Answer:
178 cm