Asked by William

In trapezoid $ABCD$, $\overline{AB}$ is parallel to $\overline{CD}$, $AB = 7$ units, and $CD = 10$ units. Segment $EF$ is drawn parallel to $\overline{AB}$ with $E$ lying on $\overline{AD}$ and $F$ lying on $\overline{BC}$. If $BF:FC = 3:4$, what is $EF$? Express your answer as a common fraction.
Answered by Reiny
Cut and paste does not work here, as you can see, but I think I followed your coding.

extend both CB and DA to meet at P
let FB = 3x, let CF = 4x, let BP= a, let FE = k
(we want k)

you now have 3 similar triangles
PBA, PFE, and PCD

a : a+3x : a+7x = 7 : k : 10

a/7 = (a+7x)/10
10a = 7a + 49x
3a = 49x
a = 49x/3

a/7 = (a+3x)/k
ak = 7a + 21x
k = (7a +21x)/a
= (7(49x/3 + 21x)/(49x/3)
= ( 343x/3 + 21x)/(49x/3)
= (406x/3) / (49x/3)
= 406/49
= 58/7

so EF = 58/7 or appr 8.29

check my arithmetic
Answered by Justin
Reiny's answer is correct, and I did check her/his computation.
Answered by AoPS
Stop cheating!
Answered by You are not AoPS
www.jiskha.com/questions/1798144/point-g-is-the-midpoint-of-the-median-xm-of-xyz-point-h-is-the-midpoint-of-xy-and-point

Stop Cheating. Really?
Answered by THE PERSON WHO PRETENDED TO BE AOPS IS :(
wow. People just need some help.
Answered by
Really, ur aops???
Answered by
Thats just dumb
Answered by
yea i highly doubt that. Nice try tho. And in the highly unlikely chance u are AOPS, well, I went to the link YOU ARE NOT AOPS posted, and that's just pathetic
Answered by Somebody
you are not AoPS, however, it is not right to cheat. anyways stop being an imposter.
Answered by asdf
pls don't cheat, but don't pose as AoPS we know ur faking fs
Answered by hmm well u dont need to k
yep its 58/7
Answered by y do you care
So what if they're cheating? It'll come back to hurt them later in life.
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