The area of a circle is equal to the area of a rectangle. The rectangle has perimeter 50 cm, and its length is 3 cm more than its breadth. What is the diameter of the circle (in cm), assuming pi = 22/7?

Introduction / Context:
This problem links two shapes by equating their areas. First, we must find the rectangle’s area using its perimeter and the relation between length and breadth. Perimeter gives L + B, and the “length is 3 cm more” condition gives L in terms of B. Solving these yields exact L and B, and therefore the rectangle area L*B. Because the circle’s area equals this rectangle area, we set pi*r^2 equal to the rectangle area and solve for r. Finally, diameter is 2*r. The value pi = 22/7 is provided to keep the radius and diameter neat and avoid messy decimals.

Given Data / Assumptions:

• Rectangle perimeter = 50 cm
• Rectangle length L = B + 3 cm
• Perimeter formula: 2*(L + B) = 50
• Area rectangle = L*B
• Area circle = pi*r^2, pi = 22/7
• Diameter = 2*r

Concept / Approach:
Find L and B from perimeter and difference, compute rectangle area, set it equal to pi*r^2, solve r, then compute diameter.

Step-by-Step Solution:
2*(L + B) = 50 => L + B = 25 L = B + 3 Substitute: (B + 3) + B = 25 => 2B = 22 => B = 11 Then L = 11 + 3 = 14 Rectangle area = L*B = 14*11 = 154 sq cm Circle area = 154 = (22/7)*r^2 r^2 = 154 * 7 / 22 = 49 => r = 7 Diameter = 2*r = 14 cm

Verification / Alternative check:
Check circle area with r=7: (22/7)*49 = 22*7 = 154 sq cm, exactly equal to rectangle area. This confirms the computed diameter is correct.

Why Other Options Are Wrong:
7 cm is the radius, not the diameter. 21 cm, 28 cm are too large and would produce areas much bigger than 154 sq cm. 10 cm is a common guess but does not match the derived radius.

Common Pitfalls:
Forgetting to divide perimeter by 2, mixing up length and breadth, forgetting to double the radius to get diameter, or using pi inconsistently.

Final Answer:
The diameter of the circle is 14 cm.