Difference between revisions of "2021 JMPSC Sprint Problems/Problem 18"
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+ | ==See also== | ||
+ | #[[2021 JMPSC Sprint Problems|Other 2021 JMPSC Sprint Problems]] | ||
+ | #[[2021 JMPSC Sprint Answer Key|2021 JMPSC Sprint Answer Key]] | ||
+ | #[[JMPSC Problems and Solutions|All JMPSC Problems and Solutions]] | ||
+ | {{JMPSC Notice}} |
Latest revision as of 16:15, 11 July 2021
Problem
On square with side length
,
is the midpoint of
. Let
be the foot of the altitude from
to
. If
can be represented as
for some integer
find the value of
Solution
Notice that since and
,
is a 45-45-90 triangle. Thus,
Also, we have
, so
which gives the answer of
.
~tigerzhang
See also
The problems on this page are copyrighted by the Junior Mathematicians' Problem Solving Competition.