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?

Perimeter of rectangle = Perimeter of square

2 (Length + Breadth) = 4 * Side

2 (40 + 22) = 4 * Side

2 * 62 = 4 * Side

Side == 31 cm

Area of rectangle = 40 * 22 = 880 cm2

Area of square = (Side)2 = 31 * 31 = 961 cm2

Therefore, the square-shaped wire encloses more area.

  • 19

you should have given the perimeter of the shape also

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First Question

First, the perimeter of the wire = Perimeter of the rectangle = 2 (l + b) = 2 x (40 cm + 22 cm) = 2 x 62 cm = 124 cm

Then, the perimeter of the square = 124 cm

The side length of the square = (124/4) cm = 31 cm

Second Question

Area of the rectangle = l x b = 40 cm x 22 cm = 880 cm^2

Area of the square = s^2 = 31 cm x 31 cm = 961 cm^2

This proves that the square encloses more area than the rectangle.

By the way, whenever you have a certain perimeter length, the largest quadrilateral that has this perimeter is always a square.

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