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Question

Question 6

A wire in the shape of a rectangle. Its length is 40 cm and breadth is 22 cm. 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

Given that the perimeter of a square and rectangle are same.
Also, length of a rectangle = 40 cm and breadth of a rectangle = 22 cm.
We know that, perimeter of a square = 4 x side
And perimeter of a rectangle = 2 (length + breadth)
According to the question:
Perimeter of square = Perimeter of rectangle
4×side = 2 (length + breadth)
4×side=2(40 + 22)
4×side = 2×62
side = 2×624= 31 cm
Thus, the side of the square is 31 cm.
Now, Area of rectangle = length×breadh
= 40×22 = 880 cm2
And area of square = side×side
= 31×31 = 961 cm2
Therefore, on comparing, the area of a square is greater than that of the rectangle.


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