Answer
The dimensions of the box:
- Height: $6$ ft
- Length: $15$ ft
- Width: $2$ ft
Work Step by Step
$Volume = 180$, $x>0$
$x(x-4)(x+9)=180$
$x(x^{2}+9x-4x-36)=180$
$x(x^{2}+5x-36)=180$
$x^{3}+5x^{2}-36x-180=0$
$x^{2}(x+5)-36(x+5)=0$
$(x+5)(x^{2}-36)=0$
$x+5=0$ or $x^{2}-36=0$
With $x+5=0$, so $x=-5$
With $x^{2}-36=0$, so $x=6$ or $x=-6$
Because $x>0$, so $x=6$
Therefore, the dimensions of the box:
- $Height=x=6$ ft
- $Length=x+9=6+9=15$ ft
- $Width=x-4=6-4=2$ ft
