2013 AMC 10B Problems/Problem 16
Revision as of 23:16, 21 February 2013 by Turkeybob777 (talk | contribs) (Fixed LaTex and added second solution)
Problem
In triangle , medians
and
intersect at
,
,
, and
. What is the area of
?
\qquad\textbf{(A)}13\qquad\textbf{(B)}13.5\qquad\textbf{(C)}14\qquad\textbf{(D)}14.5\qquad\textbf{(E)}B
1
E
AB
A
1
C
1
D
E
2
B
C
A
B
D
A
PD
2
AP
4
AD
6
CP
PE
PE=1.5
CP=3
CE=4.5
PED
3-4-5
DPE
AEDC
AD
CE
6
4.5
AEDC
6*4.5/2=\boxed{\textbf{(B)} 13.5}
DPE
P
P
2:1
AP=4
CP=3
AEDC
\frac{4\cdot 2+4\cdot 3+3\cdot 2+2\cdot 1.5}{2}=\boxed{\textbf{(B)} 13.5}$