A triangular prism has a volume of $120 \mathrm{~cm}^{3}$. Two edges of the triangular faces measure $3 \mathrm{~cm}$ and $4 \mathrm{~cm}$, as shown. The height of the prism, in $\mathrm{cm}$, is
(A) 12
(B) 20
(C) 10
(D) 16
(E) 8

![](https://cdn.mathpix.com/cropped/2024_04_20_46ead6524a8d61e21c51g-050.jpg?height=358&width=336&top_left_y=645&top_left_x=1334)
The triangular prism given can be created by slicing the $3 \mathrm{~cm}$ by $4 \mathrm{~cm}$ base of a rectangular prism with equal height across its diagonal. That is, the volume of the triangular prism in question is one half of the volume of the rectangular prism shown.

Since the volume of the triangular prism is $120 \mathrm{~cm}^{3}$, then the volume of this rectangular prism is $2 \times 120=240 \mathrm{~cm}^{3}$.

The volume of the rectangular prism equals the area of its base $3 \times 4$ times its height, $h$.

Since the volume is 240 , then $3 \times 4 \times h=240$ or $12 h=240$, so $h=\frac{240}{12}=20$.

![](https://cdn.mathpix.com/cropped/2024_04_20_748fdafcde2a47412608g-226.jpg?height=450&width=374&top_left_y=1689&top_left_x=1559)

Since the height of this rectangular prism is equal to the height of the triangular prism in question, then the required height is $20 \mathrm{~cm}$.

ANSWER: (B)