Question

In a rectangle, if the length is increased by 3 metres and breadth is decreased by 4 metres, the area of the rectangle is reduced by 67 square metres. If length is reduced by 1 metre and breadth is increased by 4 metres, the area is increased by 89 sq. metres. Find the dimensions of the rectangle.

Answer 1

Let the length= $l$ and breadth= $b$

According to the question-

Area of rectangle -

$(l+3)(b-4)=lb-67$ [$\because$ Area of rectangle $=l\times b$]
$\Rightarrow lb-4l+3b-12=lb-67$
$\Rightarrow -4l+3b=-55$
it can also be written as
$\Rightarrow 4l-3b=55$ ---(1)
Again according to the question-

Area of rectangle

$(l-1)(b+4)=lb+89$
$\Rightarrow lb+4l-b-4=lb+89$
$\Rightarrow 4l-b=93---\left(2\right)$
subtracting (2 )from (1)-

$4l-4l-3b+b=55-93$
$\Rightarrow -2b=-38$
$\Rightarrow b=19$
putting this value in equation (1), we get

$4l-3\left(19\right)=55$
$\Rightarrow 4l-57=55$
$\Rightarrow 4l=112$
$\Rightarrow l=28$
Hence, length $=28m$ breadth $=19m$