Question 60

The area of a square and a rectangle are equal. The length of the rectangle is greater than the side of a square by 5 cm and its breadth is less than the side of square by 4 cm. What will be the perimeter of the rectangle?

Solution

Let side of square = $$x$$ cm

=> Length of rectangle = $$(x+5)$$ cm and breadth = $$(x-4)$$ cm

Area of square = Area of rectangle

=> $$x^2=(x+5)(x-4)$$

=> $$x^2=x^2+x-20$$

=> $$x=20$$ --------------(i)

Thus, sides of rectangle are 25 cm and 16 cm

$$\therefore$$ Perimeter of rectangle = $$2(25+16)=82$$ cm

=> Ans - (B)

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