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In rectangle ABCD, AB=3 and BC=9 . The rectangle is folded so that points A and C coincide, forming the pentagon ABEFD. What is the length of segment EF? Express your answer in simplest radical form.

 

 Dec 14, 2019
 #1
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EF = 3*sqrt(2).

 Dec 14, 2019
 #2
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I didnt get 3sqrt(2).

 Dec 14, 2019
 #3
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Using congruent triangles and Pythagoras, EF = 4*sqrt(3).

 Dec 14, 2019
 #4
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The answer I got is sqrt10. This is how I got it (and its correct)

To begin with, let  DF=x and FA = 9-x .  is a right triangle, so we can solve for x  by applying the Pythagorean Theorem:.

Once you solved for x you can find FA=EA=5, then PE= 5-4 =1.  And Da=3 , so EF will be sqrt(9+1) or sqrt10

 Dec 15, 2019
edited by goreisthebest  Dec 15, 2019

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