anonymous
  • anonymous
Triangle, AC=20, AD=18, CE=24, AE=EB, BD=DC picture below. Find area of triangle.
Mathematics
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SOLVED
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katieb
  • katieb
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anonymous
  • anonymous
1 Attachment
King
  • King
25sqrt3?
anonymous
  • anonymous
i don't know

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Mertsj
  • Mertsj
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radar
  • radar
Is this a right triangle (
anonymous
  • anonymous
i don't know, it may be, just prove it :D
radar
  • radar
EC=24 (given) Where does the "8" fit in??
radar
  • radar
@Mersj, does the 8 in your drawing apply to EC?
anonymous
  • anonymous
i don't know how to explain in english but he's right :D but i don't know where he got 96
anonymous
  • anonymous
EF=8 not EC
Mertsj
  • Mertsj
A median divides a triangle into 2 triangles of equal area. A second median divides the triangles form by the first median into triangles whose areas are in the ratio 2:1. We can find the area of triangle ACF using Heron's formula. It is 96. So triangle CFD is 48. Together they make triangle ACD which is half the area of the entire triangle. 48+96=144 and 144 times 2 = 288 and that is the area of triangle ABC
Mertsj
  • Mertsj
No. The 8 is EF
Mertsj
  • Mertsj
Remember the intersection of medians divides the medians into 1/3 2/3 segments
radar
  • radar
Very good Mertsj, thanks for the explanation.
Mertsj
  • Mertsj
yw
anonymous
  • anonymous
ok i knew that each median divides by 1:2 but never knew that it also divides area
Mertsj
  • Mertsj
Yes. And if you drew the third median, you would have 6 triangles of equal area.

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