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Question
Fill in the blank:
A road of 108 m length is bent to form a rectangle. If the area of the rectangle is maximum, then its dimensions are _______.
Solution
A road of 108 m length is bent to form a rectangle. If area of the rectangle is maximum, then its dimensions are x = 27, y = 27.
Explanation:
Let the length and breadth of a rectangle be x and y.
∴ Perimeter of rectangle = 2(x + y) = 108
∴ x + y = 54
∴ y = 54 - x ....(i)
Let A = Area of rectangle = x × y
= x (54 - x) = 54x - x2
Differentiating w.r.t. we get
`"dA"/"dt" = 54 - 2"x"`
Consider, `"dA"/"dt" = 0`
∴ 54 - 2x = 0
∴ x = 27
∴ y = 27 ....[from (i)]
x = 27, y = 27
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