Tomas.A
Triangle, AC=20, AD=18, CE=24, AE=EB, BD=DC picture below. Find area of triangle.
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Tomas.A
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King
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25sqrt3?
Tomas.A
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i don't know
Mertsj
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|dw:1327412914643:dw|
radar
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Is this a right triangle (<ACB =90 degrees?)
Tomas.A
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i don't know, it may be, just prove it :D
radar
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EC=24 (given) Where does the "8" fit in??
radar
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@Mersj, does the 8 in your drawing apply to EC?
Tomas.A
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i don't know how to explain in english but he's right :D
but i don't know where he got 96
Tomas.A
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EF=8 not EC
Mertsj
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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
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No. The 8 is EF
Mertsj
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Remember the intersection of medians divides the medians into 1/3 2/3 segments
radar
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Very good Mertsj, thanks for the explanation.
Mertsj
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yw
Tomas.A
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ok i knew that each median divides by 1:2 but never knew that it also divides area
Mertsj
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Yes. And if you drew the third median, you would have 6 triangles of equal area.