Question

The area of a rectangle gets reduced by $80sq$ units if its length is reduced by $5$ units breadth is increasing by $2$ units if we increase the length by $10$ units and decrease the breadth by $5$ units, the area will increased by $50$ sq units. Find the length and breadth of the rectangle.

Answer 1

Let initial length and width are $l\&b$

so, Area $A_1=lb$

now from question -

$\Rightarrow A_2=(l-5)(b+2)$

$=lb+2l-5b-10$

Given $A_1-A_2=80$

$\Rightarrow -2l+5b+10=80$

$-2l+5b=70\to \left(1\right)$

$\Rightarrow A_3=(l+10)(b-5)=lb-5l+10b-50$

Given $A_3-A_1=50$

$\Rightarrow -5l+10b=100$

$-l+2b=20\to \left(II\right)$

From $\left(1\right)-2\times \left(2\right)$

$\Rightarrow b=30unit,a=40unit.$

Hence, the answer is $a=40,b=30.$