Fence cost → perimeter → dimensions:\nThe length of a rectangular plot exceeds its breadth by 20 m. If the perimeter fencing costs Rs 5300 at Rs 26.50 per metre, find the length (in metres).

Introduction / Context:
Translate total fence cost to total perimeter, then use the linear relation between length and breadth to solve the dimensions.

Given Data / Assumptions:

• Rate = Rs 26.50/m; total cost = Rs 5300 ⇒ perimeter P = 5300/26.5 = 200 m.
• L = B + 20.

Concept / Approach:
P = 2(L + B). Substitute L = B + 20 and solve for B, then get L.

Step-by-Step Solution:

Verification / Alternative check:
Perimeter check: 2(60 + 40) = 200 m; multiplied by 26.5 ⇒ Rs 5300.

Why Other Options Are Wrong:
40 and 50 are not the length; 120 is the sum of sides? Incorrect. “None of these” is not needed since the exact length is 60.

Common Pitfalls:
Forgetting to halve the perimeter when solving L + B; mixing up which side is longer.

Final Answer:
60.