Q8 of 80 Page 42

The distance around a rectangular field is 400 meters. The length of the field is 26 meters more than the breadth. Calculate the length and breadth of the field?

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

The length of the field is 26 meters more than the breadth.


∴ The length of the rectangular field = l = (x + 26) meters.


The distance around the field = 400 meters.


The distance around the field = Perimeter of the field Perimeter of rectangle = 2 (l + b)


According to the given condition,


2 (x + 26 + x) = 400


⇒ 2 (2x + 26) = 400


⇒ 4x + 52 = 400 (Removing bracket)


⇒ 4x = 400 – 52 (Transposing 52 to RHS)


4x = 348


⇒ x = (Transposing 4 to RHS)


x = 87


The breadth of the field = x = 87 meters.


The length of the field = x + 26 = 87 + 26 = 113 meters.


∴ The length and breadth of the rectangular field is 113 meters and 87 meters respectively.


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