Question

The length of a rectangle is more than its breadth
by 9cm.If the length breadth are each increased
by 3 cm, the area of new rectangle will be 64cm^2
more than that of the given rectangle .Then the
length and breadth of the rectangle are:

Answer 1

Given:

↬ A rectangle whose length is more than its breadth  by 9cm

↬ If the length breadth of rectangle are each increased  by 3 cm, the area of new rectangle will be 64cm² more than that of the given rectangle

To Find:

Length and Breadth of given rectangle

Solution:

We know that,

✏ Area of Rectangle= length×breadth

Let the length and breadth of rectangle be 'l' and 'b' respectively.

Then, According to Question

⟼ l= b+9 -----------------------(1)

Area of original rectangle= l×b

Area of new rectangle= (l+3)×(b+3)

Also, According to Question

⟼ (l+3)×(b+3)= (l×b)+64

From (1), we get

⟼ (b+9+3)×(b+3)= ((b+9)×b)+64

⟼ (b+12)×(b+3)= (b²+9b)+64

⟼ b×(b+3)+12×(b+3)= b²+9b+64

⟼ b²+3b+12b+36= b²+9b+64

⟼ b²+3b+12b+36-b²-9b-64=0

⟼ 6b-28=0

⟼ 6b= 28

$\pink{\boxed{b=\dfrac{\cancel{28}}{\cancel{6}}=\dfrac{14}{3}}}$

From (1),

⟼ l= b+9

$\rightarrow l=\dfrac{14}{3}+9$

$\rightarrow l=\dfrac{14+27}{3}$

$\orange{\boxed{l=\dfrac{41}{3}}}$

Hence,

Length of Rectangle= $\green{\dfrac{41}{3}}$

Breadth of Rectangle= $\green{\dfrac{14}{3}}$