## 10 September 2013

### Pencils down

Solve this geometry puzzle using logic only, without any calculating:
"What is the size relationship of the two yellow figures?  Is one bigger than the other (which?), or are they of identical size?"
It's not hard to guess the correct answer.  It's harder to explain why the answer must be true.

1. Jerry in and out of DallasSeptember 10, 2013 at 11:09 AM

The two yellow areas are the same area.

2. I don't believe it. I finally got one of these and can explain why without looking.

3. Holy crap pressing preview removed my answer. Not the first time it has happened to me on this site o_o gah.

A single rule solves this. Split a rectangle from corner to corner and you get two equally sized triangles. As the two large triangles have the same two smaller triangles in them the yellow left over areas will also be the same. Voilá.

My head might be conditioned to this kind of thinking... http://andreasaronsson.com/guides/perspective-drawing/divide-into-equal-parts/

4. The solution implies that the diagonal is a straight line (which is not indicated in the Figure)

1. Sure it is. I supose it might appear as "pinched" but it's a straight line.

5. "Without logic" implies illogical. I think you meant solve it without algebra.

1. Yes, really you're being asked to solve this "geometry puzzle" using Euclidean geometry, with which it's fairly easy. I'm not sure how you'd solve it by "calculating."

6. Since the triangles have the same internal angles, if you call the heights of the triangles a(big) and b(small) and their bases c(big) and d(small) then a/c = b/d = tangent of the angle between them. So ad = bc which are the areas of the 2 rectangles. So, they're the same.