Posted by Joel on October 11, 2002 at 17:14:03:
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.
I will get you started.
1. Draw a picture. Obviously you could put A, B and C anyplace, but it will be easier to see my explanation if we are both looking at the same picture. So, I put A at the top, B at the right end of the base, and C at the left end of the base. Now put D, E, and F as described in your problem. Next, drop a line from A, perpendicular to BC, meeting BC at point G. Also drop a line from F perpendicular to BC, meeting BC at H.
2. Let's call the length of BC = a, AC = b, and AB = c. Let's call the height AG = h, and the height of the small triangle (FEC) FH = x.
3. Notice that the two triangles FEC and ABC share the same angle {< ACB}. What is the sine of that angle? sin{< ACB} = h/b = x/((1/16)b)
Think about that & you will see that you now have enough information to calculate the area of triangle FEC.
You can calculate the areas of triangles EDB and DFA by the same method.
Then what?
Got it?