MathDB

2

Part of 2011 AIME Problems

Problems(2)

Rectangle and parallel lines

Source:

3/18/2011
In rectangle ABCDABCD, AB=12AB=12 and BC=10BC=10. Points EE and FF lie inside rectangle ABCDABCD so that BE=9BE=9, DF=8DF=8, BE‾∥DF‾\overline{BE} \parallel \overline{DF}, EF‾∥AB‾\overline{EF} \parallel \overline{AB}, and line BEBE intersects segment AD‾\overline{AD}. The length EFEF can be expressed in the form mn−pm\sqrt{n}-p, where m,n,m,n, and pp are positive integers and nn is not divisible by the square of any prime. Find m+n+pm+n+p.
geometryrectangleLaTeXratioAMCAIMEAoPSwiki
A square. [2011.II.2]

Source:

3/31/2011
On square ABCDABCD, point EE lies on side AD‾\overline{AD} and point FF lies on side BC‾\overline{BC}, so that BE=EF=FD=30BE=EF=FD=30. Find the area of square ABCDABCD.
geometryAMC