The area of a small rectangular plot is 84 m². If the difference between its length and the breadth is 5 m, find its perimeter.

Given:

The area of a small rectangular plot is 84 m².

The difference between its length and the breadth is 5 m.

Let the length of the rectangle be l m.

So, breadth of the rectangle = l - 5

As we know, the area of the rectangle = length x breadth

⇒ l x (l - 5) = 84

⇒ l² - 5l = 84

⇒ l² - 5l - 84 = 0

⇒ l² - (12 - 7)l - 84 = 0

⇒ l² - 12l + 7l - 84 = 0

⇒ l(l - 12) + 7(l - 12) = 0

⇒ (l - 12)(l + 7) = 0

⇒ l = 12 or - 7

Since length cannot be negative, the length will be 12 m.

So, breadth of the rectangle = (l - 5)

= (12 - 5) m

= 7 m

And, perimeter of the rectangle = 2(length + breadth)

= 2(12 + 7) m

= 2 x 19 m

= 38 m

Hence, the perimeter of the rectangle is 38 m.