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

Mathematics

1 Like

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) = $\dfrac{20}{2}$

⇒ (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

Hence, the length of the rectangular plot is 6 m or 4 m.

Answered By

2 Likes