Rectangle with breadth as a percent of length:\nThe breadth of a rectangle equals 60% of its length. If the perimeter is 800 m, find the area (in sq. m) of the field.

Difficulty: Easy

Correct Answer: 37500

Explanation:


Introduction / Context:
Linking perimeter to dimensions is standard: perimeter fixes the sum of length and breadth. Given a percentage relation between breadth and length, we can solve for both and compute area.


Given Data / Assumptions:

  • B = 0.60L.
  • Perimeter P = 800 m ⇒ 2(L + B) = 800.
  • Area A = L * B.


Concept / Approach:
Use the perimeter equation to find L + B, substitute B = 0.60L, solve for L, then compute B and multiply to obtain area.


Step-by-Step Solution:

2(L + B) = 800 ⇒ L + B = 400.With B = 0.60L: L + 0.60L = 400 ⇒ 1.60L = 400 ⇒ L = 250 m.Then B = 0.60 * 250 = 150 m.Area A = L * B = 250 * 150 = 37500 sq. m.


Verification / Alternative check:

Perimeter check: 2(250 + 150) = 2 * 400 = 800 ✔


Why Other Options Are Wrong:

47500, 57500, 77500 come from incorrect algebra or misusing percentages.


Common Pitfalls:

Using 60 as a fraction instead of 0.60.Forgetting to halve the perimeter to get L + B.


Final Answer:

37500

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