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
Jim G.
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.
#"---------------------------------------------------------------------"#
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)#
#"----------------------------------------------------------------------"#
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)#
#"-----------------------------------------------------------------"#
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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