What are the dimensions of the shaded square inside the 3-4-5 right angle triangle?
Let length of the side of the square be, a.
By similar triangles, (3a)/a = a/(4a)
(3a)(4a) = a2
a2 7a + 12 = a2
7a = 12 a = 12/7
Find the position of the square that has the maximum area.
Can you generalise for an x-y-z right angle triangle?
What would be the dimensions of the square in terms of x, y, and z?