Question

A map shows the number of steps you must take to get to a treasure. However, the map is old, and the last dimension is unreadable. Explain why the triangles are similar. How many steps do you take from the pyramids to the treasure?

Answer 1

We must take 900 steps from the pyramids to the treasure.

The triangles are similar because they are both right triangles with the same acute angle.

To see this, note that the angle at the bottom of the pyramid is a right angle, and the angle at the top of the pyramid is congruent to the angle at the bottom of the pyramid because they are alternate interior angles.

Therefore, the two triangles are similar and we can use the following proportion to solve for the number of steps from the pyramids to the treasure:

`(240)/(80) = (x)/(300)`

Cross-multiplying and solving for x, we get:

`x = (240 * 300)/(80) = 900`

Therefore, we must take 900 steps from the pyramids to the treasure.