Triangle A has sides of lengths #51 #, #48 #, and #54 #. 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
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.
Name the 3 sides of triangle B, a ,b and c , corresponding to the sides 51 ,48 ,54 in triangle A.
#"-------------------------------------------------------------------------"#
If side a = 3 then ratio of corresponding sides#=3/51=1/17#
hence b#=48xx1/17=48/17" and " c=54xx1/17=54/17#
The 3 sides of B#=(3,48/17,54/17)#
#"--------------------------------------------------------------------------"# If side b = 3 then ratio of corresponding sides
#=3/48=1/16#
hence a#=51xx1/16=51/16" and " c=54xx1/16=27/8#
The 3 sides of B#=(51/16,3,27/8)#
#"---------------------------------------------------------------------------"#
If side c = 3 then ratio of corresponding sides#=3/54=1/18#
hence a#=51xx1/18=17/6" and " b=48xx1/18=8/3#
The 3 sides of B#=(17/6,8/3,3)#
#"--------------------------------------------------------------------------"#
