Question 1148506
.
<pre>

Let x be the length of BC.  Then the length of CE is (45-x).


From the condition, you have this equation


   18^2 + x^2 = (45-x)^2 + 20^2,


saying that the two hypotenuses have equal lengths.


Simplify and find x


    18^2 + x^2 = 45^2 - 90x + x^2 + 20^2

    90x        = 45^2 + 20^2 - 18^2

    90x        = 2101

      x        = {{{2101/90}}} = 23.344...   centimeters.     <U>ANSWER</U>
</pre>

Solved.