Chapter 12.8, Problem 30HP

To determine

To describe two non-similar triangular pyramids with similar bases.

Explanation of Solution

Given:

Two non-similar triangular pyramids

Concept used:

Two pyramids are similar if their corresponding radii and heights are proportional.

Calculation:

Selecting some random values for one of the bases: $\left(3,4,5\right)$ .

Now, multiply these by a constant $2$ (say), to get the values for the similar base: $\left(6,8,10\right)$ .

These bases are in the ratio of $1:2$ .

Select a value for the height of the first pyramid: $6$

The height of the second pyramid cannot be $2\times 6=12$ .

Conclusion:

Therefore, these are the two non-similar triangular pyramids with similar bases.