Question

the perimeter of rectangle is 82 m and its area is 400 m2 . find the lenght and breadth of the rectangle.

Answer 1

Let the length and breadth of the rectangle are l and b respectively.

area of rectangle = 400 m²

so l × b = 400 ⇒ l = 400/b ........(1)

now, perimeter of rectangle = 82 m

so 2 [ l + b] = 82

⇒ l + b = 41

⇒ 400/b + b = 41 [using (1)]

⇒ b² - 41b + 400 = 0

⇒ b² - 25b - 16b + 400 = 0 [middle term split]

⇒ b(b - 25) -16(b - 25) = 0

⇒ (b - 16) (b - 25) = 0

⇒ b - 16 = 0 or b - 25 = 0

⇒ b = 16 or b = 25

When b= 16 , then l = 25

When b= 25, then l = 16

so the dimensions of the rectangle are 25m × 16m or 16m × 25m