Question

the length of a rectangle exceeds its breadth by 4 cm if the length and breadth each are increased by 3 cm the area of the new rectangle will be 18 1 square centimetre more than that of the given rectangle find the length and breadth of the given rectangle check your solution​

Answer 1

Answer:

b equals to 10 l equals to 14

Step-by-step explanation:

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.