Question

Jackie cut a piece of paper along its diagonal, forming two triangles. How do the height and base length of the two triangles compare to the height and base length of the original piece of paper?

Answer 1

For all triangles, they will always have three sets of height and base lengths.

Explanation:

As triangles are all three-sided (duh), each side can act as a base and each base will have its corresponding height (with the shortest distance to the opposite vertex).

Thus, if we were to talk about a square paper napkin with side length `a`, each triangle will have the three base-height pairs: `a` and `a`, `a` and `a`, and `sqrt(2a^2)` and `sqrt(sqrt(2a^2)+2)`.

I can't attach a diagram, so I'll have to ask an admin to double check my answer.