Discussion about math, puzzles, games and fun. Useful symbols: ÷ × ½ √ ∞ ≠ ≤ ≥ ≈ ⇒ ± ∈ Δ θ ∴ ∑ ∫ • π ƒ ¹ ² ³ °
 

You are not logged in. #1 20050618 07:53:28
Square in a triangleWhat is the largest square that can be inscribed in a 345 triangle? 2 + 2 = 5, for large values of 2. #2 20050618 09:48:24
Re: Square in a triangleWell, we could start off by making a little formula to figure out the area at any point. "The physicists defer only to mathematicians, and the mathematicians defer only to God ..."  Leon M. Lederman #3 20050619 21:17:12
Re: Square in a triangleAs an extension, find the largest (in terms of area) such rectangle. Generalise to an abc right triangle. 2 + 2 = 5, for large values of 2. #4 20050623 02:15:04
Re: Square in a triangleFirst I was wary about helping, because as you used phrases such as 'as an extension' and 'generalise', it looked suspiciously like something that you had to do for school. However, due to a combination of the facts that it has now been quite a long time, so if it was work you would most probably have handed it in by now, and you gave that cool trigonometry help thingy on the 'This is Cool' board, and it was such an interesting puzzle, I decided to help. Why did the vector cross the road? It wanted to be normal. #5 20050623 02:56:57
Re: Square in a triangleFor the extension, I used advanced calculus that I won't bore you with now (unless someone requests it), but basically, if the triangle has perpendicular sides of lengths a and b, then the biggest rectangle will always have sides of length a/2 and b/2, subject to the proof being proved that I mentioned previously. This obviously means that the rectangle will have an area of ab/4, which means that its area will also be half of that of the triangle. Why did the vector cross the road? It wanted to be normal. #6 20050623 06:04:51
Re: Square in a triangleI'm not a student  at least not in the formal sense  so no worries there! I just posted it as an interesting puzzle in its own right, and subsequently thought of the generalisation to a rectangle. 2 + 2 = 5, for large values of 2. #7 20050623 09:47:01
Re: Square in a triangleMany ways to skin a cat, hey? "The physicists defer only to mathematicians, and the mathematicians defer only to God ..."  Leon M. Lederman #8 20050623 14:05:11
Re: Square in a triangle1) Sorry for thinking that you were trying to cheat. Why did the vector cross the road? It wanted to be normal. #9 20050627 06:54:47
Re: Square in a triangle
Nor will I. It's annoying how after you do lots of complicated work to find the answer, you can tell just by looking though! Last edited by mathsyperson (20050627 06:55:48) Why did the vector cross the road? It wanted to be normal. 