The area of rectangle getsreduced by …

Let the length and breadth of the rectangle be x units and y units respectively.
Then, area of the rectangle = xy sq units.
Case I When the length is reduced by 5 units and the breadth is increased by 2 units.
Then, new length = {tex}(x - 5){/tex} units and
new breadth = {tex}(y+ 2){/tex} units.
{tex}\therefore{/tex} new area = {tex}(x - 5)(y + 2){/tex} sq units
{tex}\therefore{/tex} {tex}xy - ( x - 5)(y+ 2) = 80{/tex} {tex}\Rightarrow{/tex} {tex}5y - 2x = 70{/tex} ..... (i)
Case II When the length is increased by 10 units and the breadth is decreased by 5 units.
Then, new length = {tex}(x  + 10){/tex} units
and new breadth = {tex}(y - 5){/tex} units.
{tex}\therefore{/tex} new area = {tex}(x + 10)(y - 5){/tex}sq units.
{tex}\therefore{/tex} {tex}(x + 10)(y - 5 ) - xy = 50{/tex}
{tex}\Rightarrow{/tex} {tex}10y - 5x = 100{/tex} {tex}\Rightarrow{/tex} {tex}2y - x = 20{/tex}. ...(ii)
On multiplying (ii) by 2 and subtracting the result from (i), we get y = 30.
Putting y = 30 in (ii), we get
{tex}(2\times 30) - x = 20{/tex} {tex}\Rightarrow{/tex} {tex}60 - x = 20{/tex}

{tex}\Rightarrow{/tex} {tex}x = (60 - 20) = 40.{/tex}
{tex}\therefore{/tex} {tex}x = 40\ and\ y = 30.{/tex}
Hence, length = 40 units and breadth = 30 units.