The areas of a square and a rectangle are equal. The length

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The areas of a square and a rectangle are equal. The length of the rectangle is greater than the length of any side of the square by 5 cm and the breadth is less by 3 cm. Find the perimeter of the rectangle.

Using Rule 10,
Let the length of the side of the square be x cm.
∴ x² = (x + 5) (x – 3)
⇒ x² = x² + 5x – 3x – 15

⇒ 2x = 15 ⇒ x =	15	cm
	2

Now, length of the rectangle

= x + 5 =	15	+ 5 =	25	cm
	2		2

and breadth
=

=	15	- 3 =	15 - 6	=	9	cm
	2		2		2

∴ Required perimeter

=		25	+	9		= 2 ×	34	= 34 cm
		2		2			2