Triangle A has sides of lengths #2 ,3 #, and #9 #. Triangle B is similar to triangle A and has a side of length #1 #. What are the possible lengths of the other two sides of triangle B?

1 Answer
Jim G.
Apr 12, 2016

#(1 , 3/2 , 9/2) , (2/3 , 1 , 3) , (2/9 , 1/3 , 1)#

Explanation:

Since the triangles are similar then the ratio of corresponding sides are equal.

Name the 3 sides of triangle B , a , b and c , corresponding to the sides 2 , 3 and 9 in triangle A.
#"------------------------------------------------------------------------"#
If side a = 1 then ratio of corresponding sides #= 1/2 #
hence b = #3xx1/2 = 3/2" and " c = 9xx1/2 = 9/2#
The 3 sides of B = #(1 , 3/2 , 9/2)#
#"-----------------------------------------------------------------------"#
If b = 1 then ratio of corresponding sides #= 1/3 #
hence a#= 2xx1/3 = 2/3" and " c = 9xx1/3 = 3 #
The 3 sides of B = #(2/3 , 1 , 3)#
#"----------------------------------------------------------------------"#
If c = 1 then ratio of corresponding sides# = 1/9 #
hence a #= 2xx1/9 = 2/9" and " b = 3xx1/9 = 1/3 #
The 3 sides of B = #(2/9 , 1/3 , 1)#
#"-----------------------------------------------------------------------"#

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