1965 AHSME Problems/Problem 16
Problem
Let line be perpendicular to line . Connect to , the midpoint of , and connect to , the midpoint of . If and intersect in point , and inches, then the area of triangle , in square inches, is:
Solution
Draw , as seen in the diagram. From the problem, we know that and are medians of . Let be the midpoint of . Then, is also a median of , and it goes through 's centroid, . Because medians divide their triangle into smaller triangles of equal area, we know that . Because , . Thus, our answer is .
See Also
1965 AHSC (Problems • Answer Key • Resources) | ||
Preceded by Problem 15 |
Followed by Problem 17 | |
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