A rectangular prism has a volume of #3x^2+18x+24#. Its base has a length of #x+2# and a width of #3#. How do you write an expression that represents the height of the prism?

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Answer 1 · 2018-04-17T12:45:40

Given the volume of rectangular prism

#V=3x^2+18x+24# and it has a length #L=x+2# and width #w =3#

So its height

#H=V/(Lxxw)#

#=>H=(3x^2+18x+24)/(((x+2)xx3)#

#=>H=(3(x^2+6x+8))/(((x+2)xx3)#

#=>H=(x^2+6x+8)/(x+2)#

#=>H=(x^2+4x+2x+8)/(x+2)#

#=>H=(x(x+4)+2(x+4))/(x+2)#

#=>H=((x+4)(x+2))/(x+2)#

#=>H=x+4#