Largest square that can fit inside a triangle

[tazza]

Hi guys. I'm struggling with a question my teacher gave us in class. I need to find the largest square that can fit inside this triangle, but I have no idea where to start. Any help would be appreciated! 

[TrueTears]

The biggest square would go in the right angle of it and touch all the mid points of each line?

can you prove it?

[olly_s15]

Maybe... find angles using sine rule?
The biggest square would go in the right angle of it and touch all the mid points of each line?
Yeah? Agree? It's the maximum size.
Find the perpendiculars of each side or something haha..
Does that get you started?

Just by looking at it that triangle isn't a Pythagorean triple, so it doesn't have a right angle.

And I think you mean cosine rule.

[olly_s15]

lolz this problem is hard

[Stroodle]

lolz this problem is hard

Not if you use a good ruler.

[monokekie]

42.25 units squared? that's what i got and i don't know how my head works

[/0]

Hmmm whenever I meet a hard problem like this I go coordinate geometry on its ass
It never fails


Even though it may take over 9000 years.

[Stroodle]

I got it as 1253 pixels.

[tazza]

I used herons formula to find out the area of the triangle which is 126, then found out the height by substituting a and b into - a = 1/2b*h. 126 = 10.5h, h = 12.

I then found a formula for this question, where x(the side length of the square) = bh/b+h , 21*12/21+12, so the final answer is 84/11 for the side length, and 58.314 for the area.

I still don't understand why that formula works but it does:S