# Geometry

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.

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1. 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

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2. Reiny's answer is correct, and I did check her/his computation.

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3. Stop cheating!

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4. 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?

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5. wow. People just need some help.

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6. Really, ur aops???

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7. Thats just

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8. 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

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9. you are not AoPS, however, it is not right to cheat. anyways stop being an imposter.

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10. pls don't cheat, but don't pose as AoPS we know ur faking fs

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11. yep its 58/7

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