Triangle A has sides of lengths #24 #, #16 #, and #18 #. 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?

1 Answer
Sep 23, 2016

#(16,32/3,12),(24,16,18),(64/3,128/9,16)#

Explanation:

Anyone of the 3 sides of triangle B could be of length 16 hence there are 3 different possibilities for the sides of B.
Since the triangles are similar then the #color(blue)"ratios of corresponding sides are equal"#

Name the 3 sides of triangle B- a , b and c to correspond with the sides- 24 , 16 and 18 in triangle A.
#color(blue)"-------------------------------------------------------------"#
If side a = 16 then ratio of corresponding sides #=16/24=2/3#

and side b # = 16xx2/3=32/3," side c" = 18xx2/3=12#

The 3 sides of B would be #(16,color(red)(32/3),color(red)(12))#
#color(blue)"----------------------------------------------------------------"#
If side b = 16 then ratio of corresponding sides #=16/16=1#
and side a #=24", side c"=18#

The 3 sides of B would be #(color(red)(24),16,color(red)(18))#
#color(blue)"-----------------------------------------------------------------"#

If side c = 16 then ratio of corresponding sides #=16/18=8/9#

and side a #=24xx8/9=64/3," side b" =16xx8/9=128/9#

The 3 sides of B would be #(color(red)(64/3),color(red)(128/9),16)#
#color(blue)"-------------------------------------------------------------------"#