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EXAMPLE 4 A wire is in the shape of a square of side 10 cm. If the wire is
rebent into a rectangle of length 12 cm, find its breadth. Which encloses
more area, the square or the rectangle?
SOLUTION Side of the square = 10 cm
Length of the wire = Perimeter of the square = 4 × side = 4 × 10 cm
= 40 cm
Length of the rectangle, l = 12 cm. Let b be the breadth of the rectangle.
Perimeter of rectangle = Length of wire = 40 cm
Perimeter of the rectangle = 2 (l + b)
Thus, 40 = 2 (12 + b)
or
40
2 = 12 + b
Therefore, b = 20 − 12 = 8 cm
The breadth of the rectangle is 8 cm.
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