Triangle A has sides of lengths #15 #, #12 #, and #12 #. Triangle B is similar to triangle A and has a side of length #24 #. What are the possible lengths of the other two sides of triangle B?

1 Answer
Jim G.
Mar 14, 2016

#(24,96/5,96/5 ) ,(30,24,24), (30,24,24)#

Explanation:

Since the triangles are similar the the ratios of corresponding sides are equal.

Name the 3 sides of triangle B , a , b and c , corresponding to the sides 15 , 12 and 12 in triangle A.
#"-------------------------------------------------------------------------"#
If side a = 24 then ratio of corresponding sides# = 24/15 = 8/5 #
hence b = c #= 12xx8/5 = 96/5 #
The 3 sides in B # = (24,96/5,96/5 )#
#"-------------------------------------------------------------------------"#
If b = 24 then ratio of corresponding sides #= 24/12 = 2#
hence a #= 15xx2 = 30 " and c = 2xx12 = 24 #

The 3 sides of B = (30,24,24)
#"------------------------------------------------------------------------"#
If c = 24 will give the same result as b = 24

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