Question 1199663
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                        Step by step


<pre>

(1)  The diagonal |BD| = {{{sqrt(24^2+7^2)}}} = 25 mm.



(2)  From the area consideration, you have for the area of the triangle BCD

         {{{(1/2)*24*7}}} = {{{(1/2)*abs(BD)*abs(FC)}}}

     or

         24*7 = 25*|FC|,  which gives  |FC| = {{{(24*7)/25}}} mm.



(3)  Then from triangle CDF,  |FD| = {{{sqrt(7^2 - ((24*7)/25))^2)}}} = 

                                   = {{{sqrt((7^2*25^2-7^2*24^2)/25^2)}}} = {{{sqrt((7^2*49)/25^2)}}} = {{{49/25}}} = 1.96 mm.




(4)  Thus  |FD| = |BE| = 1.96 mm.



(5)  Hence,  |EF| = 25 - 2*1.96 = 21.08 mm = 21 {{{8/100}}} mm = 21 {{{2/25}}} mm.    <U>ANSWER</U>
</pre>

Solved.


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It can be solved in different way, using similarity of triangles.


But in my solution, there are so many nice numbers on the way, that I decided to show you THIS version.