Difference between revisions of "2012 AMC 10B Problems/Problem 19"
(→Solution) |
(→Solution) |
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Line 16: | Line 16: | ||
dot(C); | dot(C); | ||
dot(D); | dot(D); | ||
+ | label("A",(0,6),S); | ||
+ | label("B",(0,0),W): | ||
+ | label("C",(30,0),E); | ||
+ | label("D",(30,6),N); | ||
+ | draw(A--B); | ||
+ | draw(B--C); | ||
+ | draw(C--D); | ||
+ | draw(D--A); | ||
</asy> | </asy> | ||
Revision as of 14:50, 31 December 2019
Problem
In rectangle ,
,
, and
is the midpoint of
. Segment
is extended 2 units beyond
to point
, and
is the intersection of
and
. What is the area of
?
Solution
unitsize(4); pair B=(0,0); pair A=(0,6); pair C=(30,0); pair D=(30,6); dot(A); dot(B); dot(C); dot(D); label("A",(0,6),S); label("B",(0,0),W): label("C",(30,0),E); label("D",(30,6),N); draw(A--B); draw(B--C); draw(C--D); draw(D--A); (Error making remote request. Unknown error_msg)
Note that the area of equals the area of
.
Since
. Now,
, so
and
so
Therefore,
hence our answer is
See Also
2012 AMC 10B (Problems • Answer Key • Resources) | ||
Preceded by Problem 18 |
Followed by Problem 20 | |
1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25 | ||
All AMC 10 Problems and Solutions |
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions.