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.
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
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!
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