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?

Question

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?

Violet Aldrich · Accepted Answer

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

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)# #"-----------------------------------------------------------------------"#

Violet Aldrich · Answer

undefined The possible lengths of the other two sides of triangle B are  $ \frac{2}{9} $  and  $ \frac{3}{9} $, or $ \frac{2}{3} $ and 1.