The perimeter of a square is 32 cm and perimeter of a rectangle is 40 cm. If the breadth of the rectangle is 4 cm, do they have same area?

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Solution

Perimeter of square = 32 cm
4 x side = 32 cm
side = 32 $\div$ 4 = 8 cm

Area of square = side x side = 8 cm x 8 cm = 64 sq.cm

Perimeter of rectangle = 40 cm
Breadth of rectangle = 4 cm
Subtracting breadth twice from the perimeter we get
= 40 - 2 x 4
= 32 cm
32 equals to twice of the actual length.
Actual length is half of 32 cm = 32 $\div$ 2 = 16 cm

Area of reactangle = l x b
= 16 x 4
= 64 sq.cm

So, they have different perimeters but have same area.

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