A flexible wire in the form of square is bent into the form of rectangle whose length is half as much again as its breadth find percentage increase or decrease in the area of enclosed
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Step-by-step explanation:
Let the square have side length = x
Its area = x^2
Its perimeter (the length of the wire) = 4x
In the rectangle, let length = L and breadth = B
L = 3B/2
Its perimeter (the length of the wire) = 2(L + B)
= 2(3B/2 + B)
= 5B
Thus 5B = 4x
B = 4x/5
L = 3B/2 = (3/2)(4x/5) = 6x/5
The area of the rectangle = LB = (6x/5)(4x/5)
= 24x^2/25
Changing the shape from a square to a rectangle decreases its area by 1/25 = 4%
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