Rectangle with breadth 75% of length:\nThe breadth is 75% of the length. If the rectangle’s perimeter is 1050 m, find its area (in sq. m).

Difficulty: Easy

Correct Answer: 67500 sq.m

Explanation:


Introduction / Context:
Similar to related problems, a perimeter and a fixed proportional relation between sides allow us to solve for each dimension and then compute area.


Given Data / Assumptions:

  • B = 0.75L.
  • Perimeter P = 1050 ⇒ 2(L + B) = 1050 ⇒ L + B = 525.


Concept / Approach:
Substitute B = 0.75L into L + B = 525 to solve for L, then compute B and multiply to get the area.


Step-by-Step Solution:

L + 0.75L = 525 ⇒ 1.75L = 525 ⇒ L = 300 m.B = 0.75 × 300 = 225 m.Area = L * B = 300 * 225 = 67,500 sq. m.


Verification / Alternative check:

Perimeter check: 2(300 + 225) = 2(525) = 1050 ✔


Why Other Options Are Wrong:

65700, 54500, 78700 are not the product of 300 and 225 and typically stem from arithmetic mistakes.


Common Pitfalls:

Treating 75% as 0.75 is essential; mixing percentage handling often causes errors.


Final Answer:

67500 sq.m

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