Question 1209156: In the diagram, BD=15 cm and DC=6 cm. Find the ratio of the area of the parallelogram to the area of Triangle ABC.
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Answer by greenestamps(13209)   (Show Source):
You can put this solution on YOUR website!
EF and DC are congruent.
With all the given parallel line segments, triangles AEF, EBD, and ABC are all similar.
Corresponding sides EF, BD, and BC of those three triangles have lengths 6, 15, and 21, so the ratio of similarity among the three triangles is 6:15:21, or 2:5:7.
The ratio of the areas of the three triangles is the square of the ratio of similarity, which is 4:25:49.
For convenience, let the areas of the three triangles be...
AEF = 4x
EBD = 25x
ABC = 49x
The parallelogram is triangle ABC, minus triangles AEF and EBD, so the area of the parallelogram is 49x-4x-25x = 20x. So the ratio of the area of the parallelogram to the area of triangle ABC is 20x:49x = 20:49.
ANSWER: 20:49
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