Posted by Subhotosh Khan on October 12, 2002 at 10:20:40:
In Reply to: Re: Area problem posted by Soroban on October 11, 2002 at 17:31:56:
: : Huge triangle ABC has an area of 20,000,000 square feet.
: : D is on AB, E is on BC and F is on CA.
: : AD = 1/16th of AB, BE = 1/16th of BC, CF = 1/16th of CA.
: : Find area of triangle DEF.
: : Thank you.
: Hello, Bob!
: My diagram has A at the top, B at the lower-left, C at the lower-right.
: Let b = base BC of triangle ABC, let h = altitude of triangle ABC from A to BC.
: Consider triangle DFC. Its base is 15b/16.
: By similar triangles, its altitude is h/16.
I think You meant EFC
You are ascertaining ABC and EFC are similar. I have problem with that.
EC = 15/16 *a
FC = 1/16 *b
So they are not "proportional" corresponding sides. They cannot be similar.
: Hence, the area of EFC = (1/2)(15b/16)(h/16) = (15/256)(bh/2).
: That is, the area of EFC is 15/256 of the area of ABC:
: (15/256)(20,000,000) = 1,171,875
: Similarly, we can show that tringles DEB and FDA have the same area.
: Therefore, triangle DEF = 20,000,000 - 3(1,171,875) = 16,484,375 sq.ft
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