Circle vs rectangle with perimeter 50 cm The area of a circle equals the area of a rectangle whose perimeter is 50 cm and whose length exceeds its breadth by 3 cm. Find the diameter of the circle (in cm).

Introduction / Context:This problem links a rectangle (constrained by perimeter and a length–breadth relation) to a circle with equal area. We first determine the rectangle’s dimensions and area, then equate it to πr^2 to obtain the circle’s diameter.

Given Data / Assumptions:

• Perimeter of rectangle P = 50 cm
• l = b + 3 (length exceeds breadth by 3 cm)
• Area(circle) = Area(rectangle)
• Use π = 22/7 for exact integers here.

Concept / Approach:From 2(l + b) = 50 ⇒ l + b = 25. Combine with l = b + 3 to solve for l and b. Then area of the rectangle equals πr^2, allowing solution for r and thus diameter 2r.

Step-by-Step Solution:

Verification / Alternative check:Using π ≈ 3.14 gives r ≈ 7.0, keeping diameter ≈ 14 cm; integer exactness with 22/7 confirms it.

Why Other Options Are Wrong:7 cm is radius, not diameter; 21 cm and 28 cm do not match the area equivalence; only 14 cm is correct.

Common Pitfalls:Forgetting to halve perimeter to get l + b or mixing up radius/diameter leads to wrong choices.

Final Answer:14 cm