SOLUTION: The areas of two similar triangles are 144 and 81. If the base of the larger Triangle is 30, what is the corresponding base of the smaller triangle ?

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Question 752580: The areas of two similar triangles are 144 and 81. If the base of the larger
Triangle is 30, what is the corresponding base of the smaller triangle ?
Answer by KMST(5328) About Me  (Show Source):
You can put this solution on YOUR website!
WHAT YOU NEED TO KNOW:
if the ratio of lengths of sides (or any other measurement) of similar figures on a plane or 3-D solids is k,
the ratio of areas of corresponding surfaces is k%5E2, andthe ratio of corresponding volumes is k%5E3,
and viceversa.

In this case the ratio of atras is
area_of_small_triangle%2Farea_of_large_triangle=144%2F81=12%5E2%2F9%5E2=%2812%2F9%29%5E2%29
it must be that
base_of_small_triangle%2Fbase_of_large_triangle=k and
k%5E2=%2812%2F9%29%5E2 --> k=12%2F9
So base_of_small_triangle%2Fbase_of_large_triangle=12%2F9
and since base_of_large_triangle=30
base_of_small_triangle%2F30=12%2F9 --> base_of_small_triangle=30%2A12%2F9 --> highlight%28base_of_small_triangle=40%29