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A isosceles trapezoid has bases \(AB=15\) and \(CD=20\). Points \(E\) and \(F\) are on \(AD\) and \(BC\) respectively such that \(EF\parallel AB\). If \(AE:ED=2:3\), compute \(EF\).

 Dec 31, 2020
 #1
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EF = 2(2*sin30º) + 15 = 17

 Dec 31, 2020
 #2
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Where did you get 30 degrees from?

Melody  Jan 1, 2021
 #3
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+1

Here is my take.

I have added a couple of points.

 

\(\frac{TE}{2x}=\frac{2.5}{5x}\\ TE=1\\ FE=1+15+1=17 units\)

 

 Jan 1, 2021
 #4
avatar+112009 
+1

A quicker way to look at it is that the difference between 15 and 20 is 5.

EF is 2/5 of the way from the short side.

2/5 of 5 = 2

 

so the length of EF will be 15+2 =17 units

 Jan 1, 2021

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