Question

# A wire is in the shape of a rectangle. Its length is $40cm$ and breadth is $22cm.$ If the same wire is rebent in the shape of a square, what will be the measure of each side? Also, find which shape encloses more area?

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Solution

## The length of the rectangle $=40cm$The breadth of the square $=22cm$Step 1: find the side of the square. The perimeter of the square is the same as the perimeter of a rectangle$\therefore$ The perimeter of the rectangle = Perimeter of the Square $2\left(Length+Breadth\right)=4xsideofthesquare$ $2\left(Length+Breadth\right)=4×side\phantom{\rule{0ex}{0ex}}2\left(40+22\right)=4×side\phantom{\rule{0ex}{0ex}}2\left(62\right)=4×side\phantom{\rule{0ex}{0ex}}124=4×side\phantom{\rule{0ex}{0ex}}\therefore Side=\frac{124}{4}\phantom{\rule{0ex}{0ex}}Side=31cm$Step 2: Find the area of the given figures. The area of the rectangle is given by$=\left(Length×Breadth\right)$ $=40×22\phantom{\rule{0ex}{0ex}}=880c{m}^{2}$Area of square $=side×side$ $=31×31\phantom{\rule{0ex}{0ex}}=961c{m}^{2}$Therefore, a square-shaped wire encloses more area.Hence, the measure of each side of the square is $31cm$and square-shaped wired encloses more area than rectangle-shaped wired.

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