Question

The length of a rectangle exceeds its breadth by 4cm. If the length and breadth each
increased by 3cm then the area of new rectangle will be 81cm2
more than that of the
original Rectangle. Find length and breadth of original rectangle.

Answer 1

Given

• A word problems
• Based on mensuration

To find

• Length and breadth of original rectangle

Solution

Let the breadth of original rectangle be y

Therefore

Area of original rectangle = lb =Y²+4y

y (X+4)

Now According to the question

• length exceed by 4cm (y+4)
• Length and breadth increased by 3 cm
• y+3 (b)
• y+7(l)

Area of new rectangle be 81 more than Original

$\sf\implies\:(Xy+3)\times(y+7)=Y^2+4y+81$

$\sf\implies\:3(y+7)+x(y+7)=y^2+4y+81$

$\sf\implies\:3y+21+y^2+7y)=Y^2+4y+81$

$\sf\implies\:2y+1+\cancel{y^2}+7y=4y+\cancel{Y^2}+81$

=>10y-4y=81-21

=> 6y = 60

=>Y =10

Here breadth be 10 and length be 10+4 =14