2013 AMC 12A Problems/Problem 11
Revision as of 21:21, 6 February 2013 by Indianninja707 (talk | contribs) (Created page with "Let AD = x, and AG = y. We want to find DE + FG, which is nothing but x+y. Based on the fact that ∆ADE, DEFG, and BCFG have the same perimeters, we can say the following: 3x ...")
Let AD = x, and AG = y. We want to find DE + FG, which is nothing but x+y.
Based on the fact that ∆ADE, DEFG, and BCFG have the same perimeters, we can say the following:
3x = x + 2(y-x) + y = y + 2(1-y) + 1
Simplifying, we can find that
3x = 3y-x = 3-y
Since 3-y = 3x, y = 3-3x.
After substitution, we find that 9-9x-x = 3x, and x = 9/13.
Again substituting, we find y = 12/13.
Therefore, x+y = 21/13, which is C
