Question

a box has a length of 6x inches. the width equals one third the length, and the height equals half the length. if the volume equals 972 cubic inches, what does x equal?

Answer 1

Given that,

a box has a length of 6x inches

so,

• l=6x

But,the width equals one third the length

`w=(1)/(3)×6x \\\\w=2x`

again,the height equals half the length.

`h=(1)/(2)×6x \\\\h=3x`

we knows:-

Volume of a rectangle box=l×b×h

From 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.

Final solution:

.°.The value of x is 27.

Answer 2

a box has a length of 6x inches

• l=6x

the width equals one third the length

• w=
  `\sf{(1)/(3)×6x }`

• w=2x

the height equals half the length.

• h=
  `\sf{(1)/(2)×6x }`

• 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