Question

The length of a rectangle exceeds its breadth by 4cm . If the length and breadth are increased by 3cm each, the area of the new rectangle will be 81 square cm more than that of the given rectangle. Find the length and breadth of the given rectangle.

Answer 1

Hope this will help u

Answer 2

Answer:

Length = 14 cm

Breadth = 10 cm

Step-by-step explanation:

Given : The length of a rectangle exceeds its breadth by 4cm . If the length and breadth are increased by 3cm each, the area of the new rectangle will be 81 square cm more than that of the given rectangle.

To find : The length and breadth of the given rectangle?

Solution :

Let b be the breadth of the rectangle,

The length of a rectangle exceeds its breadth by 4 cm

⇒ Its length = (b+4) cm

So, the area of the original rectangle

$A=l\times b$

$A_o=b(b+4)$  

After, increasing length and breadth by 3cm

New, length= b+7 and breadth =b+3,

Thus, the new area of the rectangle is

$A_n=(b+7)(b+3)$

According to the question,

$A_n-A_o=81$

$(b+7)(b+3)-b(b+4)=81$

$b^2+7b+3b+21-b^2-4b=81$

$6b+21=81$

$6b=60$

$b=10$

Hence, the breadth of the given rectangle = 10 cm,

And, its length = 10 + 4 = 14 cm.