Can somebody please help me with these two math questions?

Question

A sculptor is planning to make two triangular prisms out of steel. The sculptor will use ABC for the bases of one prism and DEF for the bases of the other prism.

1. Is ABC similar to DEF? Explain.

2. Suppose the sculptor makes both prisms with the same height. Which prism will have a greater volume? How many times greater?

 

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Here's a link to a picture of the triangles: 

 

http://s1152.photobucket.com/user/paparoach4lifeaj/media/Screen%20Shot%202017-02-17%20at%202.04.41%20PM_zpsnj3pqwux.png.html?filters[user]=146208349&filters[recent]=1&sort=1&o=0

 

 

 

 

 

Thanks to anyone who helps!

Answer 1

1.  Yes, the are similar because if you set up a proportion for the sides of the triangles and cross-multiply, the values are the same:

 

40/48 = 30/36

 

If you cross-multiply you get 1,440 both ways

 

2.  Volume of the first prism:  

 

V = (1/2)bh_th_p

 

V = (1/2)(30)(40)h_p

 

V = 600h_p

 

Repeat this for the other prism and you will be able to answer the questions