Triangle A has sides of lengths #39 #, #45 #, and #27 #. 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
Jul 14, 2017

#(3,45/13,27/13),(13/5,3,9/5),(13/3,5,3)#

Explanation:

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.

Label the 3 sides of triangle B, a, b and c corresponding to the sides 39, 45 and 27 in triangle A.

#"--------------------------------------------------------------------------------"#
#"if a = 3 then ratio of corresponding sides "=3/39=1/13#

#rArrb=45xx1/13=45/13" and "c=27xx1/13=27/13#

#"the 3 sides of B"=(3,color(red)(45/13),color(red)(27/13))#
#"---------------------------------------------------------------------------------"#
#"if b = 3 then ratio of corresponding sides "=3/45=1/15#

#rArra=39xx1/15=13/5" and "c=27xx1/15=9/5#

#"the 3 sides of B "=(color(red)(13/5),3,color(red)(9/5))#
#"----------------------------------------------------------------------------"#
#"if c = 3 then ratio of corresponding sides "=3/27=1/9#

#rArra=39xx1/9=13/3" and " b=45xx1/9=5#

#"the 3 sides of B "=(color(red)(13/3),color(red)(5),3)#

#"-------------------------------------------------------------------------------"#