Blue Area / Red Area = ?

[Kyng]

Okay... so, I found a maths problem on Facebook. And naturally, I couldn't resist solving it . I saved the picture to my computer, and spent about 20 minutes working on a solution, then went back to Facebook to post it... only to find that, to my great annoyance, the page refreshed. And then, I was unable to find the original post again - so, I didn't get to post my solution .

At least, I didn't get to post it on Facebook! I will post it on here... but first, I'll give you guys a chance to solve it yourself . All you have to do is figure out: what is the blue area, divided by the red area?. I'll post my answer in a week's time - but, if anyone can post a correct answer before then (and show their working for it) - then, I'll give them 1,000 Coffee Credits for their efforts!

Good luck, guys .

[Kyng]

Well, it's been long enough, so here's my solution :

Spoiler

[Pyrite]

Spoiler

Just to point out a slight error in your working. The second Pythagorean calculation should equal a^2 + 4b^2, otherwise the two squares have the same area. You correct this later on so it doesn't affect the answer, but thought it was worth pointing it out for anyone following.

I took one look at this, figured it would be some business with triangles and decided it would take too long for me to work out.

[Kyng]

Spoiler

Just to point out a slight error in your working. The second Pythagorean calculation should equal a^2 + 4b^2, otherwise the two squares have the same area. You correct this later on so it doesn't affect the answer, but thought it was worth pointing it out for anyone following.

I took one look at this, figured it would be some business with triangles and decided it would take too long for me to work out.

Thanks for spotting that!

I've fixed the error now .