The problem my son wanted to work on this morning seemed fun to me:

A right triangle has hypotenuse 8 and area 8, what is the perimeter of this triangle?

The combination of algebra and geometry required to solve this problem gave my son some trouble. The first three videos below show his thought process while working through the problem. The last video is a recap of the solution he found.

(1) The first part is a struggle to find any path that leads to the solution

(2) The second part shows the struggle to find how to use the two algebraic identities that we have to help solve the problem:

(3) The third part is the solution to the problem:

(4) The last part is a recap of the solution. I was hoping that going through it one more time would help him understand a few of the ideas a little better.

That was really good, Mike. One of the things I like about it is that the problem is a perennial: What are we looking for? No, really, what are we looking for? Because regardless of context, when you don’t really know what you’re doing, that often turns out to be a really difficult thing to keep in mind. The thing is, after some of the fruitless-looking rooting around, it turns out you’ve given yourself context, so that when you remind yourself of what you’re looking for, you realize: Oh! Not over *here*, over *here*! You have something to distinguish “right area” from.
Amy

## Comments

That was really good, Mike. One of the things I like about it is that the problem is a perennial: What are we looking for? No, really, what are we looking for? Because regardless of context, when you don’t really know what you’re doing, that often turns out to be a really difficult thing to keep in mind. The thing is, after some of the fruitless-looking rooting around, it turns out you’ve given yourself context, so that when you remind yourself of what you’re looking for, you realize: Oh! Not over *here*, over *here*! You have something to distinguish “right area” from.

Amy