Question 266711
{{{drawing(400,168.4210526,-1,18,-1,7,
locate(3.7,3,6), locate(1,3,8), locate(9,6.7,12),
locate(8,4,x), locate(0,0,A), locate(15.6,6.5,C),
line(0,0,12,0), line(12,0,15.60555,6), line(15.60555,6,3.60555,6),
line(3.60555,6,0,0), green(line(3.60555,6,3.60555,0)),
green(line(3.60555,6,12.52187,.5330339))  )}}}
<pre><font size = 4 color = "indigo"><b>
The two green lines are the altitudes. The shorter one is 6.
The longer one is the unknown so it is labeled x.

Angle A = angle C because opposite angles of a parallelogram
are equal in measure.

So both right triangles are similar and their sides are 
proportional, so therefore we have the proportion:

{{{x/12=6/8}}}

Cross multiply:

{{{8x=72}}}

{{{x=9}}}

Edwin</pre>