Question

A rectangular plot has an area of 24 m². If its perimeter is 20 m, find its length.

Answer 1

Let the length and the breadth of rectangular plot be l m and b m.

Area of rectangle: l × b = 24 .....(1)

Perimeter of rectangle = 20 m

⇒ 2(l + b) = 20

⇒ (l + b) = `20/2`

⇒ (l + b) = 10

⇒ b = 10 − l

Substituting value of 'b' in equation (1), we get:

⇒ l × (10 − l) = 24

⇒ 10l − l² = 24

⇒ l² − 10l + 24 = 0

⇒ l² − 6l − 4l + 24 = 0

⇒ l(l − 6) − 4(l − 6) = 0

⇒ (l − 4)(l − 6) = 0

⇒ (l − 4) = 0 or (l − 6) = 0

⇒ l = 4 or 6.

Length of rectangle = 6 m or 4 m