Question

The length of a cuboid is $4$ m more than its breadth and $6$m more than its height. If length increased by $3$ meters, breadth increased by $4$ meters and height decreased by $2$ meters, its volume increased by $512m^3$. Find the dimensions of the cuboid.

Answer 1

Let the length be $l$.

$b=l-4,h=l-6$

Atp.

$l^{{}^{\prime }}=l+3$

$b^{{}^{\prime }}=b+4=l$

$h^{{}^{\prime }}=h-2=l-8$

also given

$l^{{}^{\prime }}{b}^{{}^{\prime }}{h}^{{}^{\prime }}=512+lbh$

$(l+3)l(l-8)=512+l(l-4)(l-6)$

$⟹(l^2-8l+3l-24)l=512+l(l^2-6l-4l+24)$

$⟹l^3-5l^2-24l=512+l^3-10l^2+24l$

$⟹5l^2-48l-512=0$

$⟹(5l+32)(l-16)$

$l=16$ as l cannot be negative.

$b=12,h=10$