2014 AMC 8 Problems/Problem 14
Problem
Rectangle and right triangle
have the same area. They are joined to form a trapezoid, as shown. What is
?
Solution
The area of is
. The area of
is
, which also must be equal to the area of
, which, since
, must in turn equal
. Through transitivity, then,
, and
. It should be apparent that
is a
triangle, so
, or
.
See Also
2014 AMC 8 (Problems • Answer Key • Resources) | ||
Preceded by Problem 13 |
Followed by Problem 15 | |
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 AJHSME/AMC 8 Problems and Solutions |
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions.