Rectangle from perimeter: The perimeter of a rectangle is 84 m and its length is 6 m more than its breadth. Find the area of the rectangle.

Difficulty: Easy

Correct Answer: 432 sq.mts

Explanation:

Introduction / Context:Standard perimeter-to-dimensions problem followed by area computation for a rectangle.

Given Data / Assumptions:

  • P = 84 m
  • L = B + 6 m

Concept / Approach:Use P = 2(L + B) to find L + B, then substitute L = B + 6 to solve. Area = L * B.

Step-by-Step Solution:

L + B = 84 / 2 = 42(B + 6) + B = 42 → 2B = 36 → B = 18 → L = 24Area = 24 * 18 = 432 sq m

Verification / Alternative check:Perimeter check: 2*(24+18) = 2*42 = 84 m. Correct.

Why Other Options Are Wrong:330, 333, 362, 384 do not equal 24*18 given the perimeter condition.

Common Pitfalls:Forgetting to halve the perimeter or miscomputing 24*18 (it is 432).

Final Answer:432 sq.mts

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