Answer:
5 inches
Explanation:
Let the length of the box = l
Width of the box = 2 inches less than the length
= l - 2
Height of the box = 3 inches less than the length
= l - 3
Volume of the box is given by length * width * height
=
![\[l * (l-2) * (l-3)\]](https://img.qammunity.org/2021/formulas/mathematics/middle-school/qol9hcpk9d55f7x4cxts5ymmnl73pte04q.png)
=
![\[l * (l^(2)-5l+6)\]](https://img.qammunity.org/2021/formulas/mathematics/middle-school/d8yt2sv79vsdyfeui86m3jbuxhoi0xjlkr.png)
=
![\[l^(3)-5l^(2)+6l)\]](https://img.qammunity.org/2021/formulas/mathematics/middle-school/lwg6ep50n59hrmdhytyuc3h073jdzipmju.png)
= 30 cubic inches
Factorizing 30 yields 30 = 2*3*5
This is of the form l * (l-2) * (l-3) where l = 5
So the length of the box is 5 , width is 3 and height is 2 inches respectively.