 # In a rectangle, if the length is increased by 3 meters and breadth is decreased by 4 meters, the area of the rectangle is reduced by 67 square meters Question:

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

Solution:

Let the length and breadth of the rectangle be and units respectively

Then, area of rectangle = square units

If the length is increased by meters and breath is reduced each by square meters the area is reduced by square units

Therefore,

$x y-67=(x+3)(y-4)$

$x y-67=x y+3 y-4 x-12$

$y y-67=y y+3 y-4 x-12$

$4 x-3 y-67+12=0$

$4 x-3 y-55=0 \cdots(i)$Then the length is reduced by meter and breadth is increased by meter then the area is increased by square units

Therefore,  Thus, we get the following system of linear equation

$4 x-3 y-55=0$

$4 x-y-93=0$

By using cross multiplication we have

$\frac{x}{(-3 \times-93)-(-1 \times-55)}=\frac{-y}{(4 \times-93)-(4 \times-55)}=\frac{1}{(4 \times-1)-(4 \times-3)}$

$\frac{x}{279-55}=\frac{-y}{-372+220}=\frac{1}{-4+12}$

$\frac{x}{224}=\frac{f y}{-152}=\frac{1}{8}$

$x=\frac{224}{8}$

$x=28$

and

$y=\frac{152}{8}$

$y=19$

Hence, the length of rectangle is meter,

The breath of rectangle is meter.