Question

A wire is 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

According to the question,

Perimeter of square = Perimeter of rectangle

⇒ 4 x side = 2 (length + breadth)

⇒ 4 x side = 2 (40 + 22) ⇒ 4 x side = 2 x 62

⇒ side = (2 x 62)/4 = 31 cm

Thus, the side of the square is 31 cm.

Now, Area of rectangle = length x breadth = 40 x 22 = 880 cm² 

And Area of square = side x side = 31 x 31 = 961 cm²

Therefore, on comparing, the area of square is greater than that of rectangle.