Question

A box is 1 meter wider than its height and 2 meters longer than his width.

Answer 1

Let the height be $x$

Hence, the width is $x+1$ and length is $(x+1)+2=x+3$

The volume is given to be 2 m³

Hence, $2=x(x+1)(x+3)$

Solving,

$x^3+4x^2+3x-2=0$

$(x+2)(x^2+2x-1)=0$

$\implies x+2=0$ or $x^2+2x-1=0$

But $x=-2$ cannot be possible

Hence, $x^2+2x-1=0$

$\implies x=-1-\sqrt 2$ or $x=-1+\sqrt 2$

Reject the negative solution.

Hence, the height is $\sqrt 2-1$,

width is $\sqrt 2$ and length is $\sqrt 2 +2$