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
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)"-------------------------------------------------------------------"#