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The perimeter of a rectangle is 40 cm. Find the dimensions of the rectangle if its area is maximum. |
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Answer» Let l and b are the sides of rectangle. ` :. 2(l+b) = 40 ` `rArr l+b = 20` …(1) If the area of rectangle is A, then `A= l*b` `l(20-l)` [From eq. (1)] `=20 l - l^(2)` `rArr (dA)/(dl) = 20 - 2l` For maxima/minima `(dA)/(dl) = 0` ` rArr 20 - 2l=0` ` rArr l = 10 cm` And `(d^(2)A)/(dl^(2)) = - 2 lt 0` `:." At " l = 10 cm`, is maximum. Therefore, for maximum area, the sides of rectangle are 10 cm and 10 cm. |
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