Difference between revisions of "2021 JMPSC Invitationals Problems/Problem 10"
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==Solution== | ==Solution== | ||
− | + | t is implied <math>P</math> lies on the line that bisects <math>AB</math> and <math>DC</math>. We have the area of the trapezoid is <math>16 \cdot 16=256</math> since the height is <math>16</math>. Now, subtracting <math>144</math> we have <math>224=4x+28(16-x)</math> for <math>x</math> is the height of <math>\triangle PAB</math>. This means <math>x=\frac{28}{3}</math>, asserting the area of <math>\triangle PAB</math> is <math>\frac{56}{3} \implies 56+3=\boxed{59}.</math> ~Geometry285 | |
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Revision as of 17:17, 11 July 2021
Problem
A point is chosen in isosceles trapezoid
with
,
,
, and
. If the sum of the areas of
and
is
, then the area of
can be written as
where
and
are relatively prime. Find
Solution
t is implied lies on the line that bisects
and
. We have the area of the trapezoid is
since the height is
. Now, subtracting
we have
for
is the height of
. This means
, asserting the area of
is
~Geometry285
See also
- Other 2021 JMPSC Invitationals Problems
- 2021 JMPSC Invitationals Answer Key
- All JMPSC Problems and Solutions
The problems on this page are copyrighted by the Junior Mathematicians' Problem Solving Competition.