Mathematics
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.
Answer
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.
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