SOLUTION: A trapezoid of area 100 cm^2 has bases 5 cm and 15 cm. Find the areas of the two triangles formed by extending the legs until they intersect.

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Question 1113959: A trapezoid of area 100 cm^2 has bases 5 cm and 15 cm. Find the areas of the two triangles formed by extending the legs until they intersect.
Answer by greenestamps(13200) About Me  (Show Source):
You can put this solution on YOUR website!


We can find the height of the trapezoid, knowing its area and the lengths of its bases:
100+=+%28%2815%2B5%29%2F2%29%2Ah
100+=+10h
h+=+10

When the legs of the trapezoid are extended until they intersect, two similar triangles are formed, the small triangle with height x and the large triangle with height (10+x).

Since the two triangles are similar, the ratio of their heights is the same as the ratio of their bases:
x%2F%28x%2B10%29+=+5%2F15
5x%2B50=15x
10x=50
x=5

So the small triangle has base 5 and height 5; its area is (1/2)(5)(5) = 25/2.

The large triangle has base 15 and height 10+5=15; its area is (1/2)(15)(15) = 225/2.