2008 Mock ARML 1 Problems/Problem 6
Problem
Square has side length . is the midpoint of , and is the midpoint of . is on such that is between and , and . Compute the length of .
Solution
By the Pythagorean Theorem, and . Let . By the Law of Cosines on , The Law of Cosines on yields
The Angle Bisector Theorem on yields Substituting,
See also
2008 Mock ARML 1 (Problems, Source) | ||
Preceded by Problem 5 |
Followed by Problem 7 | |
1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 |