Sharing Catriona Shearer’s geometry puzzles with my younger son – part 11

Catriona Shearer shared a great puzzle this morning.

Four of the five squares are congruent. What’s the ratio of red to purple? pic.twitter.com/dog7l1jlwv

— Catriona Shearer (@Cshearer41) April 23, 2020

This one is a bit more difficult than others I’ve shared with my son lately, but he wanted to give it a try. He wasn’t able to solve it, but we talked about the progress me had and the ideas he had:

Next we looked at a geometric solution given by Phillip Gibbs as well as comment to Gibbs’s tweet from Dr. Rick. These tweets showed a really clever geometric solution to the problem.

I loved this but struggled to follow the argument at first, so for the sake of similarly slow others, here's my take on your idea.

Three identical pink triangles yields 30 for angle.

Half red area (slightly transformed) and half purple shown, cut into identical triangles. 🙂 pic.twitter.com/RMb2oXrFXd

— Dr Rick (@rfbooth) April 23, 2020

Here’s what my son had to say about these solutions:

Finally, I showed my son how to see that the triangles in the picture were, indeed, 30-60-90 triangles. This is a little bit of algebra, but I thought it would be important for him to see why those triangles were there.

I really love this problem and was happy that the thread had some great geometric solutions. Even though my son wasn’t able to get this one solved all the way, I think he learned a lot working through it.