Question

The area of a rectangle gets reduced by 80 sq. units if its length is reduced by 5 units and the breadth is increased by 2 units. If we increase the length by 5 units and decrease the breadth by 2 units, the area is increased by 60 sq. units. Represent the above situation algebraically and graphically.

Answer 1

Step1: Framing a relationship between length and breadth.

Let the length of rectangle be $x$ units

Breadth of rectangle be $y$ units.

Area of rectangle = length$\times$ breadth

=$xy$ sq. units

When length is reduced by $5$units,

we get the new length as $x-5$ units

When breadth is increased by $2$ units,

we get the new breadth as $y+2$ units

According to the given condition,

$(x-5)(y+2)=xy-80$

$xy+2x-5y-10=xy-80$

$2x-5y=-70$ …………….(1)

From second condition,

when length is increased by $5$ units,

we get the new length as $x+5$

When breadth is decreased by $2$ units,

we get the breadth as $y-2$

$(x+5)(y-2)=xy+60$

$-2x+5y=70$…………………..(2)

Pair of equations (1) and (2) represent the situation algebraically,

Step 2:Graphical Representation

Equation (1) and (2) are same hence form coinciding lines.

$$\begin{gathered} 2x=5y-70 \\ y=\frac{1}{5}\left(2x+70\right) \end{gathered}$$

Substituting $-5,0$and $5$ for $x$ values we get $y$ values as follows.

$x$	$-5$	$0$	$5$
$y$	$12$	$14$	$16$

Plotting the points on a graph ,we get graphical representation of the situation as given below.

Hence the situation represented algebraically and graphically.