The perimeter of a rectangular field is 82 m and its area is 400 m2. F

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

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

Answer»

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