Question

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?

Answer 1

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
$\Rightarrow$ $4\times side$ = 2 (length + breadth)
$\Rightarrow$ $4\times side=2(40+22)$
$\Rightarrow$ $4\times side=2\times 62$
$\Rightarrow$ $side=\frac{2\times 62}{4}=31cm$
Thus, the side of the square is 31 cm.
Now, Area of rectangle = $length\times breadh$
= $40\times 22=880c{m}^2$
And area of square = $side\times side$
= $31\times 31=961c{m}^2$
Therefore, on comparing, the area of a square is greater than that of the rectangle.