Triangle A has sides of lengths 60 , 45 , and 54 . Triangle B is similar to triangle A and has a side of length 7 . What are the possible lengths of the other two sides of triangle B?

1 Answer
Apr 12, 2016

(7 , 21/4 , 63/10) , (28/3 , 7 , 42/5) , (70/9 , 35/6 , 7)

Explanation:

Since the triangles are similar the the ratios of corresponding sides are equal.

Name the 3 sides of triangle B , a , b and c , corresponding to the sides 60 , 45 and 54 in triangle A.
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If side a = 7 then the ratio of corresponding sides = 7/60
hence b =45xx7/60 = 21/4" and " c = 54xx7/60 = 63/10
The 3 sides of B =(7 , 21/4 , 63/10)
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If b = 7 then ratio of corresponding sides = 7/45
hence a = 60xx7/45 = 28/3" and " c = 54xx7/45 = 42/5
The 3 sides of B = (28/3 , 7 , 42/5)
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If c = 7 then ratio of corresponding sides = 7/54
hence a =60xx7/54 = 70/9" and " b = 45xx7/54 = 35/6
The 3 sides of B =(70/9 , 35/6 , 7)
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