Q11 of 58 Page 118

Sum of the areas of two squares is 468m2. If the difference of their perimeters is 24m, find the sides of the two squares.

Let the side of one square be x, another square be (x + 6)

Sum of Areas = 468 m2


x2 + (x + 6)2 = 468


2x2 + 12x - 432 = 0


⇒ x2 + 6x - 216 = 0


Performing factorization we get:


⇒ x2 + 18x - 12x - 216 = 0


⇒ x(x + 18) - 12(x + 18) = 0


⇒ (x - 12)(x + 18) = 0


⇒ x = 12, - 18


Neglecting the negative value , we get


Side of squares = 12 m ,18 m


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