Triangle A has sides of lengths #12 #, #9 #, and #6 #. Triangle B is similar to triangle A and has a side with a length of #16 #. What are the possible lengths of the other two sides of triangle B?

Question

Triangle A has sides of lengths #12    #, #9    #, and #6     #. Triangle B is similar to triangle A and has a side with a length of #16     #. What are the possible lengths of the other two sides of triangle B?

Evelyn Arboleda · Accepted Answer

(16,12,8), (#64/3,16,32/3 ) , (32,24,16) # 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 12,9 and 6 in triangle A. #"---------------------------------------------------------------------------"# If side a = 16 then ratio of corresponding sides # = 16/12 = 4/3# hence # b = 9xx4/3 = 12" and " c = 6xx4/3 = 8# The 3 sides of B = (16 , 12 , 8 ) #"--------------------------------------------------------------------------"# If side b = 16 then ratio of corresponding sides # = 16/9 # hence a =# 12xx16/9 = 64/3" and " c = 6xx16/9 = 32/3 # The 3 sides of B #=(64/3 , 16 , 32/3 ) # #"--------------------------------------------------------------------------"# If c = 16 then ratio of corresponding sides = #16/6 = 8/3 # hence a#= 12xx8/3 = 32" and " b = 9xx8/3 = 24 # The 3 sides of B = (32 , 24 , 16 ) #"-----------------------------------------------------------------------------"#

Autumn Armstrong · Answer

undefined The possible lengths of the other two sides of triangle B are 12 and 9.