Mid Point Massacre?

Geometry Level 4

In triangle △ A B C \triangle ABC , D D is an altitude on B C BC and length of B C BC is 24. E E , F F and G G are the midpoints of B D BD , A C AC and B C BC respectively.If the area of triangle △ F G C \triangle FGC is 30 30 , what is the length of E F EF ?

5√11 5√15 5√13 13√3 2+√2 13 5√73

Parinaya Chaturvedi by Parinaya Chaturvedi , 24, India

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2 solutions

1 Helpful 0 Interesting 0 Brilliant 0 Confused
Akash Deep
Jul 13, 2015

please correct the details . According to me the area of FGC should be given as 30 then only we obtain the answer as 13 and this question appeared in FTRE 2014 class 9. just construct FM perpendicular to BC and by mpt you get the value of FM as half of AD and we already can find AD. now we also know EM = 12 and so using pythagorous theorem in triangle FEM we get EF = 13.

0 Helpful 0 Interesting 0 Brilliant 0 Confused

@Parinaya Chaturvedi I agree that we need FGC to be 30, and have made the corresponding edit. If you disagree, please submit your solution.

Calvin Lin Staff - 4 years, 9 months ago

no the details are absolutely correct!!! and i have not copied it from FTRE...... I have made this question 2 years ago when i was in class 9

Parinaya Chaturvedi - 5 years, 11 months ago

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sorry 4 years ago not 2 years .....

Parinaya Chaturvedi - 5 years, 11 months ago

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