CA Foundation · Quantitative Aptitude · Differential and Integral Calculus
A rectangular enclosure is to be built using 80 metres of fencing for all four sides. The maximum possible area of the enclosure in square metres is:
The maximum area is 400 square metres. With perimeter 80, the sides are x and 40 − x, so area is 40x − x². This is maximised at x = 20, giving a square of side 20 and area 400.
- A300
- B400Correct
- C1,600
- D800
Explanation
Let sides be x and 40 − x. Area A = x(40 − x) = 40x − x². A' = 40 − 2x = 0 gives x = 20, and A'' = −2 < 0. Area = 20 × 20 = 400. 1,600 comes from wrongly using 40² as the area.
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