a rectangle prism has a volume of 3x^2 + 18x+ 24. its base has a length of x + 2 and width of 3, what expression represents the

height of the prism

Mathematics

1 answer:

OlgaM077 [116]3 years ago

6 0

$\bf \textit{volume of a rectangular prism}\\\\
V=lwh\qquad 
\begin{cases}
l=x+2\\
w=3\\
V=3x^2 + 18x+ 24
\end{cases}\implies \cfrac{V}{lw}=h
\\\\\\
\cfrac{3x^2 + 18x+ 24}{3(x+2)}=h\implies \cfrac{\underline{3}(x^2 + 6x+ 8)}{\underline{3}(x+2)}=h
\\\\\\
\cfrac{(x+4)\underline{(x+2)}}{\underline{(x+2)}}=h\implies x+4=h$

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