Triangle A has sides of lengths #51 #, #48 #, and #54 #. Triangle B is similar to triangle A and has a side of length #3 #. What are the possible lengths of the other two sides of triangle B?

Question

Triangle A has sides of lengths #51    #, #48    #, and #54     #. Triangle B is similar to triangle A and has a side of length #3     #. What are the possible lengths of the other two sides of triangle B?

Evelyn Arboleda · Accepted Answer

#(3,48/17,54/17),(51/16,3,27/8),(17/6,8/3,3)# Since triangle B has 3 sides , anyone of them could be of length 3 and so there are 3 different possibilities. Since the triangles are similar then the ratios of corresponding sides are equal. Name the 3 sides of triangle B, a ,b and c , corresponding to the sides 51 ,48 ,54 in triangle A. #"-------------------------------------------------------------------------"# If side a = 3 then ratio of corresponding sides #=3/51=1/17# hence b#=48xx1/17=48/17" and " c=54xx1/17=54/17# The 3 sides of B #=(3,48/17,54/17)# #"--------------------------------------------------------------------------"# If side b = 3 then ratio of corresponding sides #=3/48=1/16# hence a#=51xx1/16=51/16" and " c=54xx1/16=27/8# The 3 sides of B #=(51/16,3,27/8)# #"---------------------------------------------------------------------------"# If side c = 3 then ratio of corresponding sides #=3/54=1/18# hence a #=51xx1/18=17/6" and " b=48xx1/18=8/3# The 3 sides of B #=(17/6,8/3,3)# #"--------------------------------------------------------------------------"#