Question

triangular prism is placed on the top of a rectangular prism such that they both share a common base. If both the prisms have the same volume, then how many times the height of the rectangular prism must be the height of the triangular prism?

• A. one-fourth
• B. twice
• C. half
• D. thrice

Answer 1

The correct option is B twice


Let be the height of the 𝑝 triangular prism.
Let 𝑙, 𝑤, and ℎ be the length, width, and the height of the rectangular prism.
Volume of the triangular prism = Volume of the rectangular prism

$(\frac{1}{2}\times w\times p)\times l=l\times w\times h$

$\frac{1}{2}\times p=h$

$p=2h$

Thus, the height of the triangular prism must be twice the height of the rectangular prism.