Question

The length of a Rectangle is $8m$ less than thrice its width. If area of the Rectangle is $1675sqm$. Find the length and width of the Rectangle

Answer 1

Given,

$l=3b-8$

$A=1675m^2$

$A=l\times b$

$1675=(3b-8)\times b$

$1675=3b^2-8b$

$3b^2-8b-1675=0$

$b=\frac{-b\pm b^2-4ac}{2a}$

$=\frac{8\pm (-8{)}^2-4(3\left)\right(-1675)}{2\left(3\right)}$

$=\frac{8\pm 142}{6}$

$b=25,-\frac{67}{3}$

$\therefore b=25m$

$\therefore l=3b-8=3\left(25\right)-8=67m$