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Global Maxima

The perimeter...

Question

The perimeter of a rectangle is 100 metres. Find the length of its sides when the area is maximum.

x = 20, y = 30

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x = 23, y = 27

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x = 25, y = 25

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x = 28, y = 22

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Solution

The correct option is B $x = 25, y = 25$
$2 (x + y) = 100, A = x y = x (50 - x)$
A will be maximum when $x = 25$ ,
$∴ y = 25$ i.e., it is a square.
Ans: C

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