Triangle A has sides of lengths #27 #, #12 #, and #18 #. 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?

1 Answer
Feb 16, 2016

There are three solutions, corresponding to assuming each of the 3 sides is similar to the side of length #3#: #(3,4/3,2),(27/4,3,9/2),(9/2,2,3)#

Explanation:

There are three possible solutions, depending on whether we assume the side of length #3# is similar to the side of #27, 12# or #18#.

If we assume it is the side of length #27#, the other two sides would be #12/9=4/3# and #18/9=2#, because #3/27=1/9#.

If we assume it is the side of length #12#, the other two sides would #27/4# and #18/4#, because #3/12=1/4#.

If we assume it is the side of length #18#, the other two sides would be #27/6=9/2# and #12/6=2#, because #3/18=1/6#.

This could be represented in a table.