1987 AIME Problems/Problem 6
Problem
Rectangle is divided into four parts of equal area by five segments as shown in the figure, where
, and
is parallel to
. Find the length of
(in cm) if
cm and
cm.
Solution
Since and
and the areas of the trapezoids
and
are the same, the heights of the trapezoids are the same. Thus both trapezoids have area
. This number is also equal to one quarter the area of the entire rectangle, which is
, so we have
.
In addition, we see that the perimeter of the rectangle is , so
.
Solving these two equations gives .
See also
1987 AIME (Problems • Answer Key • Resources) | ||
Preceded by Problem 5 |
Followed by Problem 7 | |
1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 | ||
All AIME Problems and Solutions |