Maths-
General
Easy

Question

An orange crate is in the shape of a rectangular prism . It has a volume of 3 x cubed plus 7 x squared plus 2 x cubic units and has a base area of x squared plus 2 x square units. Find the height of the orange crate ?.

hintHint:

The Volume of a rectangular prism is: straight V equals whl , where w, h & l are width , height and length respectively.
The base area of a rectangular prism is:straight A equals lw  .
We are asked to find the height of the rectangular prism.

The correct answer is: Hence, the height of the prism is: 3x + 1.


    Step 1 of 2:
    The volume of a rectangular prism is:3 straight x cubed plus 7 straight x squared plus 2 straight x
    The general formula is:
    table attributes columnalign right columnspacing 0em end attributes row cell straight V equals wlh space space space space space space space space space space space space space space space space end cell row cell equals 3 straight x squared plus 7 straight x squared plus 2 straight x end cell end table
    The base of the prism is:straight x squared plus 2 straight x .
    The general formula is,
    table attributes columnalign right columnspacing 0em end attributes row cell straight A equals straight w space space space space space end cell row cell equals straight x squared plus 2 straight x end cell end table
    Step 2 of 2:
    Dividing the volume by the base area, we have the height. That is;
    table attributes columnalign right columnspacing 0em end attributes row cell straight V over straight A equals fraction numerator straight w divided by straight h over denominator Ih end fraction end cell row cell equals straight h space space space space space space space space end cell end table
    Substituting the values in the equation, we have:
    table attributes columnalign right columnspacing 0em end attributes row cell straight V over straight A equals fraction numerator 3 straight x cubed plus 7 straight x squared plus 2 straight x over denominator straight x squared plus 2 straight x end fraction end cell row cell equals fraction numerator straight x open parentheses 3 straight x squared plus 7 straight x plus 2 close parentheses over denominator straight x left parenthesis straight x plus 2 right parenthesis end fraction space space space end cell end table
    table attributes columnalign right columnspacing 0em end attributes row cell equals fraction numerator 3 straight x squared plus 6 straight x plus straight x plus 2 over denominator left parenthesis straight x plus 2 right parenthesis end fraction space space space space end cell row cell equals fraction numerator 3 straight x left parenthesis straight x plus 2 right parenthesis plus 1 left parenthesis straight x plus 2 right parenthesis over denominator straight x plus 2 end fraction end cell row cell space space space end cell end table
    table attributes columnalign right columnspacing 0em end attributes row cell equals fraction numerator left parenthesis 3 straight x plus 1 right parenthesis left parenthesis straight x plus 2 right parenthesis over denominator straight x plus 2 end fraction end cell row cell equals 3 straight x plus 1 space space space space space space space space space space space space end cell end table
    Hence, the height of the prism is: 3x + 1.

    Dividing two expressions and multiplying it with reciprocal of the second expression has the same effect.

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