Q9 of 80 Page 42

The length of a rectangular field is 8 meters less than twice its breadth. If the perimeter of the rectangular field is 56 meters, find its length and breadth?

Let the breadth (b) of the rectangular field be x meters.

∴ Twice of the breadth = 2x meters.


The length of the field is 8 meters less than twice the breadth.


∴ The length of the field = l = (2x – 8) meters.


The perimeter of the rectangular field = 56 meters.


Perimeter of rectangle = 2 (l + b)


According to the given condition,


2 (2x – 8 + x) = 56


⇒ 2 (3x – 8) = 56


6x – 16 = 56


⇒ 6x = 56 + 16 (Transposing 16 to RHS)


6x = 72


⇒ x = (Transposing 6 to RHS)


x = 12


The breadth of the field = x = 12 meters.


The length of the field = 2x – 8 = 2 (12) – 8 = 24 – 8


= 16 meters.


∴ The length and breadth of the rectangular field is 16 meters and 12 meters respectively.


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