Question

the base of the other prism.
Is ∆ABC similar to ∆DEF? Explain.
A sculptor is planning to make two triangular prisms out of steel. The sculptor will use ∆ABC for the base of one prism and ∆DEF the base of the other prism. Suppose the sculptor makes both prisms with the same height. Which prism will have a greater volume? How many times greater? Show your work.

(picture below)

Answer 1

 if they are similar then their sides are proportional and the following would be true: 
40/30 = 48/36 
reduce both sides: 
4/3 = 4/3 
so, yes, they are similar. 

Answer 2

Answer:

The volume prism with base DEF is 1.44 times greater that volume prism with base ABC.

Step-by-step explanation:

In triangle ABC and DEF,

$\frac{AB}{DE}=\frac{40}{48}=\frac{5}{6}$

$\frac{BC}{EF}=\frac{30}{36}=\frac{5}{6}$

$\frac{AB}{DE}=\frac{BC}{EF}$

$\angle B=\angle E=90^{\circ}$               (Given)

By SAS rule of similarity,

$\triangle BCA\sim \triangle EFD$

Therefore ∆ABC similar to ∆DEF.

Let the height of both prism are same, i.e., h.

Area of prism is

$A=\text{Area of base}\times h$

$\frac{\text{Area of prism with base EFD}}{\text{Area of prism with base BCA}}=\frac{A(\triangle EFD)\times h}{A(\triangle BCA)\times h}=\frac{\frac{1}{2}\times 36\times 48}{\frac{1}{2}\times 30\times 40}=\frac{36}{25}=1.44$

Therefore the volume prism with base DEF is 1.44 times greater that volume prism with base ABC.