Question

If the length of a certain rectangle is decreased by 4 cm and the width is increased by 3 cm, a square with the same area as the original rectangle would result. Find the perimeter of the original rectangle.

Answer 1

Let length $=l$ length $=\omega \Rightarrow$

$\left(1\right)l-4=\omega +\mathrm{3...}\left(1\right)$

$\Rightarrow l=\omega +7$

$\left(2\right)l.\omega =(l-4)(\omega +3)$

$(\omega +7)\left(\omega \right)=(\omega +3{)}^2$

${\omega }^2+7\omega ={\omega }^2+9+6\omega$

$\omega =9\Rightarrow l=16$

$\therefore$ Perimeter $=2(l+\omega )$

$=2(9+16)=2\times 25$

$=50m$