Chapter 12.5, Problem 2CE

To determine

Tocheck:Whether the given solids are similar or not.

Answer to Problem 2CE

Yes, the given solids are similar.

Explanation of Solution

Given information:

The given solids are shown below:

  

The bases of both shapes is triangle and similar. Length of one of the side of the first prism is $9$ and the length of corresponding side of second prism is $6$ .

So, the ratio of the sides of both the prisms is:

  $9:6=3:2$

Length of second side of the first prism is $12$ and the length of corresponding side of second prism is $8$ .

So, the ratio of the sides of both the prisms is:

  $12:8=3:2$

Length of third side of the first prism is $12$ and the length of corresponding side of second prism is $8$ .

So, the ratio of the sides of both the prisms is:

  $12:8=3:2$

The height of the first prism is equal to $15$ and the height of second prism is equal to $10$ .So, the ratio of the heights of both the prisms is:

  $15:10=3:2$

The ratio of all the corresponding sides of both the prisms is equal.

Therefore, the given solids are similar.