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Area of Square

Find the maxi...

Question

Find the maximum area of a rectangle of perimeter $176$ $c m$ .

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Solution

$L e t t h e l e n g t h o f r e c t a n g l e b e x, t h e n w i d t h = (176 / 2 - x) = (88 - x) ∴ A r e a = A = x (88 - x) = 88 x - x^{2} n o r f o r a r e a t o b e m a x i m u m, (\frac{d A}{d x}) = 0 88 - 2 x = 0 o r x = 88 / 2 = 44 ∴ m a x i m u m a r e a = x (88 - x) = 44 (88 - 44) = 44^{2} = 1936 s q u n i t$

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