Answer:
4 cm.
Step-by-step explanation:
Given:
A box has a volume of 308 cm cubed.
Its height is 4 cm greater than its length.
Its length is 3 cm greater than its width.
Question asked:
What is the width of the box?
Solution:
Let width = [tex]x\ cm[/tex]
Length = [tex]x+3\ cm[/tex]
Height = [tex]x+3+4=x+7\ cm[/tex]
As we know:
[tex]Volume\ of\ box=length\times width\times height[/tex]
[tex]308=(x+3)\times x\times(x+7)\\ \\ 308=(x^{2} +3x)(x+7)\\ \\ 308=x^{2} (x+7)+ 3x(x+7)\\ \\ 308=x^{3} +7x^{2} +3x^{2} +21x\\ \\ 308=x^{3} +10x^{2} +21x\\ \\ Subtract\ 308\ from\ both\ sides\\ \\ x^{3} +10x^{2} +21x-308=0\\ \\ factor\ left\ side\ of\ equation\\ \\ (x-4)(x^{2} +14x+77)=0\\ \\ Set\ factors\ equal\ to\ 0.\\ \\ x-4=0 \ or\ x^{2} +14x+77=0\\ \\ \\[/tex]
As width can never be in negative, [tex]x= 4\ cm[/tex]
By substituting the value:-
Width = [tex]x\ cm[/tex] = 4 cm
Thus, width of the box is 4 cm.
