Question

The length of rectangle exceeds its breadth by 9cm. If the length and breadth are each increased by 3cm, the area of a new rectangle will be 84cmsq more than that of the given rectangle. Find the length and breadth of the given rectangle.

Answer 1

breadth=x+12cm
lenght=x+3cm
area=l×b
x+12×x+3=84cm sq
2x +15=84cm sq
2x=84-15
x=69/2
x=34.5
length= x+3cm
=34.5+3cm
=37.5cm
breadth=x+12 cm
= 34.5 +12cm
=46.5cm

Answer 2

Given:

Length= 9(Breadth)

To Find:

Length and breath of the given rectangle

Solution:

Let, the breadth of a rectangle be x cm

Then,its length will be (x+9) cm

Area of the given rectangle=[x{x+9}]$cm^{2}$

New breadth of the rectangle=(x+3) cm

New length of the rectangle=[(x+9)+3]cm=[x+12] cm

Area of new rectangle=[(x+12)(x+3)]$cm^{2}$

According to the question,

(Area of new rectangle)-(Area of given rectangle)=84$cm^{2}$

 $(x+12)(x+3)-x(x+9)=84\\(x^{2}+15x+36)-(x^{2}+9x)=84\\6x+36=84\\6x=48\\x=\dfrac{48}{6}\\x=8$

Thus, breadth=8 cm

length=(8+9) cm=17cm

• ∴The required length and breadth of a rectangle is 17 cm and 8 cm respectively.