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This problem trains for: SAT-I, AMC-8, GMAT.

In a scalene triangle ABC the midpoints of the sides are denoted with M, N, P. If the area of triangle MNP is 17 square units what is the area of triangle ABC. (figure not to scale)

figure

Since M, N, P are midpoints, the triangles ABC and MNP are similar and the similarity ratio is:

equation

Therefore, the areas of the two triangles are in a ratio:

equation

If the area of triangle MNP is 17 the area of the triangle ABC can be found by solving:

equation