Justin Does Math

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41

Also, to be clear: my solution didn’t involve drawing any extra lines or putting multiple figures together. I assume they couldn’t have intended anything like Elliot’s solution for students using a paper book. And I know from experience that geometry type problems are sometimes purposely drawn not-to-scale and with inaccurate angles, so that students can’t just uses rulers, etc, to solve. So you can’t count on things being equal just because they look equal. So I figured out a solution that is solvable with basic triangle rules & the information they gave you.

Edit: re my solution, triangle rules aren’t the only rules I used. it also involves some other rules that you usually know by the time you know about similar triangles, before they teach pythagorean. I don’t wanna go into too much detail though incase it is spoilery.

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I can give another hint if you need.

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ok go ahead :slight_smile:

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Ignore the lines which are edges of the original square, e.g. AB.

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Also, list all the different shapes you can find that are new (visible in the bigger pic but not the original). Not sure what you’re doing but the goal is just to find more/any.

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I found a square

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So you could write down the components of that square and also try to connect its total area to anything else.

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it has 1 black square, 3 small triangles, and 3 trapezoids, so it must be smaller than our original square

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what else do you know about it? one of your main problems seems to be you’ll figure out one or two things and stop instead of brainstorming more.

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I’m not sure what else I can say about it.

The information regarding the length of the sides that we have is for the perimeter, and I’m not using the pythagorean theorem, so I don’t think I can say anything specific about the dimensions of the sides.

I don’t think we have enough information to figure out the actual area. I guess we can say that it’s 1 small triangle + 1 trapezoid smaller than 400.

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That is information. You figure things out and somehow give up on them. You can use what you’ve said to make some formulas and do algebra.

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o

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I assume this is because the pythagorean is not part of the intended solution.

But I don’t think Elliot’s solution is part of the intended solution either.

(Tho, I don’t think pythagorean is needed for Elliot’s solution.)

Edit: I said this because I’m not sure if this is possibly creating other problems with your solution - like, maybe there are other things you are avoiding without saying, that would make Elliot’s solution easier. Or if you are trying to do Elliot’s solution with some other unstated assumptions that you think the intended solution requires, but that don’t apply to Elliot’s solution. (Like, it just seems kind of weird that you are 1, trying to follow the “rules” of the intended solution, but then 2, attempting to do Elliot’s solution, which I am pretty sure is not the intended solution. And that contradiction could be creating some problems for you.)

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There is more I could say, btw. I was just waiting for feedback/questions before saying more.

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me2

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Using your stuff from earlier

Let S = black square, T = small triangle, and P = trapezoid

Original square: 400 = 1S + 4T + 4P
New Square: 400 - (T + P) = 1S + 3T + 3P

I’m not sure how to do a useful algebraic manipulation here. It seems like I need more info.

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You can maybe see why you need more info from that formula, which would give you ideas about what to look for. Or just find more things and write them down.

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ok

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Did you find any other squares?

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well there are three others similar to that first one (this image might be a little unclear but hopefully u get the idea)

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