Q1 of 33 Page 41

The perimeter of a rectangle is 80 metres and its length is one metre more than twice the breadth. What are its length and breadth?

Let the breadth of the rectangle be x metres.

Twice the breadth = 2x metres


One more than twice the breadth = 2x + 1 metres


∴ Length of the given rectangle = 2x + 1 metres


Perimeter of the rectangle = 80 metres (given)


⇒ 2(length + breadth) = 80


⇒ 2(2x + 1 + x) = 80


⇒ 2(3x + 1) = 80 (Transporting 2 to RHS)


⇒


⇒ 3x + 1 = 40


⇒ 3x = 40-1


⇒ 3x = 39


⇒


⇒x = 13


Hence,


Length of the rectangle = 2x + 1 = 2 × 13 + 1 = 27 metres


Breadth of the rectangle = x = 13 metres


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