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Question
A rod of 108 meters long is bent to form a rectangle. Find its dimensions if the area is maximum. Let x be the length and y be the breadth of the rectangle.
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Solution
∴ 2x + 2y = 108
∴ y = 54 - x
Now, area of rectangle = xy =x (54 - x)
∴ f(x) = 54x -x2
f ' (x) = 54 -2x
f '' (x) = -2
For extreme values f '( x) = 0
∴ 54 - 2x = 0
∴ x = 27
f '' (27) = -2 < 0 ∴ Area is maximum when x =27 , y = 27
∴ The dimensions of rectangle are 27m × 27m
It is a square.
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