Answer :
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a box has a length of 6x inches
- l=6x
the width equals one third the length
- w=[tex]\sf{\dfrac{1}{3}×6x }[/tex]
- w=2x
the height equals half the length.
- h=[tex]\sf{\dfrac{1}{2}×6x }[/tex]
- h=3x
we know that,
Volume of a rectangle box=l×w×h
According to the question,
if the volume equals 972 cubic inches,
- l×w×h=volume
- 6x × 3x × 2x=972
- 36x^3=972 cubic unit
- x=972/36
- x=27
Therefore:-
The value of x is 27.