Rectangle & Perimeter from Fencing Cost — Length:breadth = 5:3. Total fencing cost is ₹ 3,000 at ₹ 7.50 per meter. Find the difference (length − breadth).

Introduction / Context:Perimeter of a rectangle determines fencing length; cost per meter allows us to reverse-calculate the perimeter and then the side lengths using the given ratio. Finally, compute the difference of the two sides.

Given Data / Assumptions:

• L:B = 5:3
• Total fencing cost = ₹ 3,000
• Rate = ₹ 7.50 per meter

Concept / Approach:Perimeter P = total cost / rate. With L = 5x, B = 3x ⇒ P = 2(L + B) = 2(8x) = 16x. Solve x from P, then compute L − B.

Step-by-Step Solution:P = 3,000 / 7.50 = 400 m16x = 400 ⇒ x = 25L = 5x = 125 m; B = 3x = 75 mDifference = 125 − 75 = 50 m

Verification / Alternative check:P = 2(125 + 75) = 400; cost = 400 * 7.50 = 3,000 ✔

Why Other Options Are Wrong:100, 150, 200 m are multiples of x but not equal to L − B; 25 m is half the correct difference.

Common Pitfalls:Using L:B = 5:3 but computing 2(5x + 3x) incorrectly; or using area instead of perimeter.

Final Answer:50 m