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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

The perimeter of the rectangle = Perimeter of the Square

2(Length+Breadth)=4xsideofthesquare

2(Length+Breadth)=4×side2(40+22)=4×side2(62)=4×side124=4×sideSide=1244Side=31cm

Step 2: Find the area of the given figures.

The area of the rectangle is given by=(Length×Breadth)

=40×22=880cm2

Area of square =side×side

=31×31=961cm2

Therefore, a square-shaped wire encloses more area.

Hence, the measure of each side of the square is 31cmand square-shaped wired encloses more area than rectangle-shaped wired.


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