Sunday, December 17, 2006

One Of My Turns

Another math problem...answer coming in a couple of days or after the first correct answer in the comments section:

Angle ABC = Angle DEA
length AB = 3
BC = 4
AE = 1

What is the length of line segment ED?

3 comments:

Kimota94 aka Matt said...

I'll give this one a try.

Based on the info you provided, angles ABC + BCA + CAB = 180 because they form a triangle. Also, angles EAD + ADE + DEA = 180, for the same reason.

We're told that angle DEA = angle ABC, and we can see that angles CAB and EAD are the same angle, so therefore equal.

Therefore, angles BCA and ADE must be equal, as well, making triangles AED and ABC similar triangles.

That means that the ratio of sides AB to AE would be equal to the ratio of sides BC to ED, or 3/1 would be equal to 4/ED, meaning ED would be 4/3.

How'd I do, Prof Hinckley?

Jimmy said...

Excellent! I'll try something a touch more difficult next time.

vishrut said...

Similar triangles.. 1/x=3/4
x= 4/3
I wasted a minute dropping a perpendicular line from D to AC.

Very GMAT like question :)