Answer :
Answer:
5 inches
Step-by-step 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
= [tex]\[l * (l-2) * (l-3)\][/tex]
= [tex]\[l * (l^{2}-5l+6)\][/tex]
= [tex]\[l^{3}-5l^{2}+6l)\][/tex]
= 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.