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I am wondering how you would go about to find the largest square that would fit inside a triangle?
An example of what i am asking is:
What is the side length of the largest square that would fit inside a right angled triangle with the sides 5,12, and 13?
Any help would be appreciated
Medusa
The largest rectangle that would fit inside a right triangle with the sides 5, 12, 13 is a square. Let the square have side x. By Pythagorean theorem,Solving the equation gives x = 60/17.
Thank you for the help. I trying to use this method but i kept stuffing up the second part. You have made it a lot clearer now.
Thanks
Medusa
After doing further research into this question and many discussions with my math genius friends i was wondering if anyone could explain how the formula: bh/b+h works in this situation? b = base, h = height. I am unsure how this works and any help explaining it would be appreciated.
Hello, Medusa!
Quote:
Can anyone explain how the formula: bh/(b+h) works in this situation?
b = base, h = height.
Code:- - Ao
: : | *
: h-x | *
: : | *
: - Do-------oE
h : | x | *
: : | | *
: x | x| *
: : | | *
: : | | *
- - o-------o-------------o
B - x - F - - b-x - - C
: - - - - b - - - - :
We have right triangle ABC with AB = h, BC = b.
We have square BDEF with sides x.
Since ∆ABC ~ ∆ADE, we have:
. . .h. . . .h - x
. . --- .= .----- . . → . . hx .= .b(h - x) . . → . . hx .= .bh - bx
. . .b. . . . . x
. . bx + hx .= .bh . . → . . (b + h)x .= .bh
. . . . . . . . . . . . . . .bh
Therefore: . x .= .-------
. . . . . . . . . . . . . .b + h
So the formula would work for a right angled triangle.. What about if the triangle was isoceles? Would the formula still work if the triangle isn't right angled is pretty much what i am asking.
Medusa
1. Draw a sketch. see attachmentQuote:
Originally Posted by Medusa
2. Use similar triangles. You'll get the proportions:
http://latex.codecogs.com/png.latex?...dfrac{bh}{b+h}
Thanks for the help :) I sat there and worked it out using your advice and it makes sense after completely working it out by hand :) Thanks for help
Medusa