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Question

A wire when bent in the form of a square encloses an area 676cm2. Find the largest area enclosed by the same wire when bent to form a rectangle whose adjacent sides differ by 4 cm.

A
672cm2
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B
672m2
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C
6.72cm2
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D
67.2cm2
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Solution

The correct option is A 672cm2
Let x be the side of the square.
The area of the square =x2

Given, the area of square =576 cm2
x2=576x=26

Now, the length of the wire = perimeter of the square with side as 26 cm=4x=4×26=104 cm

Let y be the length of the rectangle.
breadth of the rectangle =y4

Since the same wire is used to bend in the form of a rectangle,
Perimeter of the rectangle =104 cm
2(y+y4)=104
2y4=52
y2=26
y=28

Area of rectangle =28(284)=672 cm2

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