Posted by Soroban on October 11, 2002 at 17:31:56:
In Reply to: Area problem posted by Bob on October 11, 2002 at 16:07:52:
: 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.
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