Algebraic or Geometric?

[follybard]

This evening at dinner, in the process of answering the very important question, "How far is Dunkin Donuts from here?" spouse asked, "So, wait, if you double both the legs of a right triangle, does the hypotenuse also double

Comments

[drangelo]

I would have done exacly what kingtheseus did - use the formula with known numbers, then double the numbers and see if that works. Assuming I didn't just think about the situation and say "of course". But if I wanted to *teach* someone how to figure it out, I would likely do both what kingtheseus suggests and what you drew.

[immlass]

If forced to prove it, I would have drawn pretty pictures.

[javenallese]

The geometric proof using similar triangles came to mind first for me.

My second thought was trigonometric.

My last thought was Pythagorean.

If I were to be showing this to someone I would use both approaches used by you and your husband. Some people understand better one way and others the other.

[notshakespeare]

A friend of mine was a high school physics teacher for a half year before he had to quit. He had a problem trying to teach his kids the metric system.

When you first proposed this, I instantly knew the answer, because I realized you could easily change the units without modifying any graph or formula.