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

[olofd]

I did it most like Kadath, but if I wanted to explain to someone else I would probalby do it with some similarity argument. (Which is much more general than just for triangles, even if engineers use them mostly for triangles.)

[la_directora]

My approach would have been more algebraic, but only because knowing the formula for the Pythagorean theorem makes that seem the obvious way to do it. I would have basically pulled out paper and pen and tried to confirm that (2a)^2 + (2b)^2 = (2c)^2. Though in my head I was already thinking, "Well of course it does."

And as an extravert, I'm totally amused about your annoyance at spouse working the problem out loud. Given that I probably would have done the same. :)

[kid_lit_fan]

IAWTC. While I am more mathematically inclined than average, I am far from a mathematician, I would've started working it aloud, and gone to paper and pen to make sure because math-in-my-head only works so well (and I tend to doubt myself.).

[drives_a_mini]

Definitely geometric. I am a visual learner. While I didn't actually do it because that would mean I was doing math when no one was forcing me (ick), my mind would have begun to draw the picture then I would have had to actually draw it to finish finding the solution.

If someone had tried to explain this through algebra, I would have needed the geometric picture to truly understand it. You're picture was perfect, btw. Makes total sense. :-)

[kingtheseus]

I was almost certain of the answer already, I'd just want visual proof.

My answer to it would have been draw one triangle, with numbers in it 3, 4 and 5, since that was my favourite triangle when I studied it in high school. I'd then double everything to see if those numbers still worked in the formula. I worked out something kind of interesting about what the relationship between the numbers on all three sides was, I'm struggling to remember what it was now. It's only been 22 years.

[omorka]

Me: Yes. Duh.

Teacher-Me: Show your work.

Me: *sigh* Okay. Doubling the length of each leg of a right triangle doesn't change the tangent ratio of the two legs, ergo the angles do not change, ergo the triangles are similar, ergo the scale factor for the hypotenuse is also 2.

If I had to follow that up, I'd use the formula.