A letter F is composed of 6 unit squares and two rectangles of unit width as in the figure:
Find the lengths of the two rectangles such that the center of gravity is at the center of the middle square.
(In reply to
re: maybe  numerical confirmation and question by Charlie)
>How does one analytically solve the two simultaneous quadratics?
I don't know: this particular one could be simplified.
Let's L1 and L2 are the lenghts of the upper and lower rectangles and
x=0.5+L1/2
y=0.5+L2/2
Setting the origin (0,0) at the center of the square which is left from the gravity center, we will get the following eqs:
2x^2x2y3=0
2y^2+y4x3=0
Subtracting one from the other:
2(x^2y^2) +3x3y=0 then
2(xy)(x+4)=0 then
x=y

Posted by Art M
on 20070517 19:56:14 