SOLUTION: In the rectangle ABCD, what is the distance from point E to point F, in mm? Image: https://imgur.com/a/BhD0Rcc

Algebra ->  Rectangles -> SOLUTION: In the rectangle ABCD, what is the distance from point E to point F, in mm? Image: https://imgur.com/a/BhD0Rcc      Log On


   

Question 1199663: In the rectangle ABCD, what is the distance from point E to point F, in mm?
Image: https://imgur.com/a/BhD0Rcc
Found 2 solutions by greenestamps, ikleyn:
Answer by greenestamps(13200) About Me  (Show Source):
Answer by ikleyn(52781) About Me  (Show Source):
You can put this solution on YOUR website!
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                        Step by step 


(1)  The diagonal |BD| = sqrt%2824%5E2%2B7%5E2%29 = 25 mm.



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

         %281%2F2%29%2A24%2A7 = %281%2F2%29%2Aabs%28BD%29%2Aabs%28FC%29

     or

         24*7 = 25*|FC|,  which gives  |FC| = %2824%2A7%29%2F25 mm.



(3)  Then from triangle CDF,  |FD| = sqrt%287%5E2+-+%28%2824%2A7%29%2F25%29%29%5E2%29 = 

                                   = sqrt%28%287%5E2%2A25%5E2-7%5E2%2A24%5E2%29%2F25%5E2%29 = sqrt%28%287%5E2%2A49%29%2F25%5E2%29 = 49%2F25 = 1.96 mm.




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



(5)  Hence,  |EF| = 25 - 2*1.96 = 21.08 mm = 21 8%2F100 mm = 21 2%2F25 mm.    ANSWER

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.