2022 SSMO Team Round Problems/Problem 5
Problem
Consider the following rectangle where
If
find the value of
(Note that
is the area of
.)
[asy] unitsize(0.25cm); dot((0,0)); dot((12,0)); dot((12,16)); dot((0,16)); draw((0,0)--(12,0)--(12,16)--(0,16)--(0,0)--cycle); dot((8,22)); dot((17,4)); dot((8,16)); dot((12,4)); label("", (0,0), SW); label("
", (12,0), SE); label("
", (12,16), NE); label("
", (0,16), NW); label("
", (8,22), NE); label("
", (17,4), SE); label("
", (8,16), SE); label("
", (12,4), SW); draw((8,22)--(8,16),dashed+linewidth(.5)); draw((12,4)--(17,4),dashed+linewidth(.5)); [/asy]