The perimeter of a rectangular field is 82 m and its area is 400 m2. Find the breadth of the rectangle.

Perimeter of a rectangle = 2(l + b)


Area of the rectangle = l × b


Given, perimeter of a rectangular field is 82 m and its area is 400 m2


Let the breadth be ‘a’ m and length be ‘b’ m


2(a + b) = 82


b = 41 – a


Also, a × b = 400


a × (41 – a) = 400


a2 – 41a + 400 = 0


a2 – 25a – 16a + 400 = 0


a(a – 25) – 16(a – 25) = 0


(a – 16)(a – 25) = 0


a = 16, 25


Assuming breadth to smaller, thus breadth = 16m


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