Question

If the length of a rectangle is increased by $5$ metres and breadth decreased by $3$ metres , the area would decrease by $5$ square metres. If the length is increased by $5$ square metres. If the length is increased by $3$ metres and breadth increased by $2$ metres, the area would increase by $50$ square metres. What are the length and breadth?

Answer 1

Let length be ${}^{\prime }{a}^{\prime }$m

breadth be ${}^{\prime }{b}^{\prime }$m

area ${}^{\prime }a{b}^{\prime }{m}^2$

$(a+5)(b-3)=ab-5\Rightarrow ab+5b-3a-15=ab-5\Rightarrow 5b-3a=10-\left(1\right)(a+3)(b+2)=ab+50\Rightarrow ab+6+3b+2a=ab+50\Rightarrow 3b+2a=144-\left(2\right)$

solving equation $\left(1\right)$ and $\left(2\right)$

$19b=152\Rightarrow b=\frac{152}{19}=85\times 8-3a=10\Rightarrow 3a=40-10=30\Rightarrow 3a=30\Rightarrow a=10$