Triangle A has sides of lengths #36 #, #48 #, and #18 #. 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
Sep 24, 2016

#(3,4,3/2),(9/4,3,9/8),(6,8,3)#

Explanation:

Any of the 3 sides of triangle B could be of length 3 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"#

Let the 3 sides of triangle B be a ,b and c, corresponding to the sides 36 ,48 and 18 in triangle A.
#color(blue)"-------------------------------------------------------------------"#
If side a = 3 then ratio of corresponding sides #=3/36=1/12#

hence side b #=48xx1/12=4" and side c" =18xx1/12=3/2#

The 3 sides of B would be #(3,color(red)(4),color(red)(3/2))#
#color(blue)"----------------------------------------------------------------------"#
If side b = 3 then ratio of corresponding sides #3/48=1/16#

a #=36xx1/16=9/4" and side c" =18xx1/16=9/8#

The 3 sides of B would be #=(color(red)(9/4),3,color(red)(9/8))#
#color(blue)"-----------------------------------------------------------------------"#
If side c = 3 then ratio of corresponding sides #=3/18=1/6#

hence #a=36xx1/6=6" and b" =48xx1/6=8#

The 3 sides of B would be #=(color(red)(6),color(red)(8),3)#
#color(blue)"-------------------------------------------------------------------------"#