The length of a rectangle exceed its breadth by 3 cm if each of the length and breadth are increased by 2 cm the area of the new rectangle will be 58 cm sq.more than that of the original rectangle find the length and breadth of the original rectangle
Answers
Let's assume the breadth of the rectangle be x cm
The length of the rectangle = x + 3 cm
It is given that the length and breadth of the rectangle is increased by 2.
Now, the breadth of the rectangle = x + 2
The length of the rectangle = x + 3 + 2 = x + 5
It is also given that the area of the rectangle is 70 sq. cm
Therefore, the area of the rectangle = length x breadth = (x + 2)(x + 5) = 70
⇒ x2 + 5x + 2x + 10 = 70
⇒ x2 + 7x = 70 - 10
⇒ x2 + 7x = 60
⇒ x2 + 7x - 60 = 0
⇒ x2 + 12x - 5x - 60 = 0
⇒ x( x + 12) -5(x + 12) = 0
⇒ ( x + 12) (x - 5) = 0
either, or,
(x + 12 = 10 x - 5 = 0
⇒ x = 10 - 12 = -2 ⇒ x = 5
The breadth of a reactangle is never negative, therefore the value of x = 5 cm
Hence, the breadth of the rectangle = 5 cm
The length of the rectangle = 5 + 3 = 8 cm
hope it helps