Question 923994
Here is a triangle (triangle BCD) of base 6cm and height 1cm,
but it may not be your triangle.
Since the shape of the triangle was not specified,
I made mine an isosceles triangle of base 6cm).
I cut four squares out of it.
Does the size of the square matters?
The largest square I could make is the blue square.
Its side measures {{{6/7}}}
{{{drawing(700,200,-3.5,3.5,-0.5,1.5,
triangle(-3,0,0,0,0,1),triangle(0,0,3,0,0,1),
arrow(-0.1,1,4.5,1),arrow(3,0,4,0),
blue(line(-3/7,0,-3/7,6/7)),blue(line(3/7,0,3/7,6/7)),
blue(line(-3/7,6/7,3/7,6/7)),blue(line(-3/7,0,3/7,0)),
green(line(-.5,.5,0,0)),green(line(-.5,.5,0,1)),
green(line(.5,.5,0,0)),green(line(.5,.5,0,1)),
red(line(0,1,0.75,0.75)),red(line(0.5,0,0.75,0.75)),
red(line(0,1,-0.25,0.25)),red(line(0.5,0,-0.25,0.25)),
rectangle(1,0.1,1.1,0.2), locate(-0.05,-0.3,6),
arrow(-0.1,-0.4,-3,-0.4),arrow(0.1,-0.4,3,-0.4),
arrow(3.1,0.6,3.1,1),arrow(3.1,0.4,3.1,0),locate(3.05,0.58,1),
locate(-0.05,0,A),locate(-3.05,0,B),
locate(-0.05,1.15,C),locate(2.95,0,D),
locate(0.379,0,E),locate(0.379,1,F)
)}}}
BD=6 and AC=1 are the base and height of BCD
AC=(1/2)BD=3
ACD and DEC are similar right triangles, with leg lengths in the ratio of 1:3.
The side of the blue triangle is DE,
and AD=(1/2)DE.
With the 1:3 ratio, DC=3DE,
and since AD+DC=3,
(1/2)DE+3DE=3
DE+6DE=6
7DE=6
DE=6/7