Question

the length of the rectangle exceeds is breadth by the 3 CM if the length and the breadth are each increased by 2 cm then the area of a new rectangle will be 70 square CM more than that of the given rectangle find the length and breadth of the rectangle

Answer 1

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

so,
x + 12 = 10 and x - 5 = 0
⇒ x = 10 - 12 = -2 and ⇒ x = 5

Hence,

as the breadth of a reactangle is never negative,

therefore the value of x = 5 cm

the length of the rectangle = 5 + 3 = 8 cm

Answer 2

let breadth be x cm, then length=x+3cm

area of rectangle=l*b

x(x+3)=area of rectangle 1

(x+2)(x+5)=area of rectangle 2

⇒x²+3x+70=x²+7x+10+

⇒4x=60

⇒x=15cm,x+3=18cm

∴length=18cm, breadth=15cm