Question 725887
<pre>
{{{drawing(400,2800/13,-5,8,-1,6,
locate(3.2,0,7),locate(.1,2.5,5),locate(-1.8,0,x),
triangle(-25/7,0,0,0,0,5),triangle(0,0,0,5,7,0) )}}}

The altitude to the base of a right triangle divides
the right triangle into two smaller triangles which are
similar to each other and to the whole given triangle.

Also the altitude to the base of a right triangle 
is a mean proportion between the two segments it divides
the hypotenuse into.

Therefore,

                   {{{x/5}}}{{{""=""}}}{{{5/7}}}
                  {{{7x}}}{{{""=""}}}{{{25}}}
                   {{{x}}}{{{""=""}}}{{{25/7}}}

Hypotenuse = {{{x + 7}}}{{{""=""}}}{{{25/7}}}{{{""+""}}}{{{7/1}}} = {{{25/7}}}{{{""+""}}}{{{49/7}}}{{{""=""}}}{{{74/7}}}{{{""=""}}}{{{10.6}}}

Edwin</pre>