Find the dimensions of a rectangle whose perimeter is 28 meters and wh

1.	Find the dimensions of a rectangle whose perimeter is 28 meters and whose area is 40 square meters.
Answer» Let the length of the rectangle = x Given perimeter = 2(1 + b) = 28 ⇒ (1 + b) = 28/2 = 14 Breadth of the rectangle = 14 – x Area = length . breadth = x (14 – x) = 14x – x² By problem, 14x – x² = 40. ⇒ x² – 14x + 40 = 0 ⇒ x² – 10x – 4x + 40 = 0 ⇒ x(x – 10) – 4(x – 10) = 0 ⇒ (x – 10) (x – 4) = 0 ⇒ x – 10 = 0 (or) x – 4 = 0 ⇒ x = 10 (or) 4 ∴ Length = 10 m or 4 m Then breadth = 14 – 10 = 4 m (or) 14 – 4 = 10 m

Find the dimensions of a rectangle whose perimeter is 28 meters and whose area is 40 square meters.

Answer»

Let the length of the rectangle = x

Given perimeter = 2(1 + b) = 28

⇒ (1 + b) = 28/2 = 14

Breadth of the rectangle = 14 – x

Area = length . breadth = x (14 – x)

= 14x – x²

By problem, 14x – x² = 40.

⇒ x² – 14x + 40 = 0

⇒ x² – 10x – 4x + 40 = 0

⇒ x(x – 10) – 4(x – 10) = 0

⇒ (x – 10) (x – 4) = 0

⇒ x – 10 = 0 (or) x – 4 = 0

⇒ x = 10 (or) 4

∴ Length = 10 m or 4 m

Then breadth = 14 – 10 = 4 m (or) 14 – 4 = 10 m