The breadth of a rectangular field is 75% of its length. If the perimeter of the field is 1050 m, what is the area of the field (in sq m)?

Introduction / Context:
This problem tests basic mensuration for rectangles using perimeter and a relationship between length and breadth. The key idea is to convert the percentage statement into an algebraic relationship, use the perimeter formula to find the actual dimensions, and then compute area. Because a rectangle's perimeter depends only on the sum of length and breadth, once we express breadth in terms of length (or vice versa), we can solve in one clean equation. After the dimensions are known, area is simply length * breadth. This is a standard one-equation substitution problem that rewards careful unit handling (metres and square metres).

Given Data / Assumptions:

• Breadth is 75% of length
• Perimeter = 1050 m
• Rectangle perimeter formula: P = 2*(L + B)

Concept / Approach:
Convert 75% into a multiplier: B = 0.75*L. Use the perimeter to solve for L, then compute B, then area = L*B.

Step-by-Step Solution:
Let length = L m, breadth = B m B = 75% of L = 0.75*L Perimeter: 2*(L + B) = 1050 => L + B = 525 Substitute B: L + 0.75L = 525 => 1.75L = 525 L = 525 / 1.75 = 300 m B = 0.75*300 = 225 m Area = L*B = 300*225 = 67500 sq m

Verification / Alternative check:
Check perimeter using found dimensions: 2*(300+225)=2*525=1050 m, which matches. So the dimensions are correct, and the area computed from them is reliable.

Why Other Options Are Wrong:
65700 and 70500 come from arithmetic slips in 300*225. 54500 and 78700 result from incorrect L and B due to wrong handling of 75% or perimeter.

Common Pitfalls:
Using 75% as 75 (instead of 0.75), forgetting to divide perimeter by 2, or mixing up which dimension is 75% of the other.

Final Answer:
The area of the field is 67500 sq m.