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