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geometry intermediate
Problem
The midpoints of the sides of a triangle with area are joined to form a triangle with area . What is the ratio of to ? Express your answer as a common fraction.
Solution
When you connect the midpoints of two sides of a triangle, you get a segment which is half as long as the third side of the triangle. Therefore, every side in the smaller triangle is the side length of the original triangle. Therefore, the area of the smaller triangle is the area of the larger triangle.
Final answer
\frac{1}{4}