Triangle A has sides of lengths #27 #, #15 #, and #21 #. 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

The sides of Triangle B are either 9, 5, or 7 times smaller.

Explanation:

Triangle A has lengths of 27, 15, and 21.

Triangle B is similar to A and has one side of side 3. What are the other 2 side lengths?

The side of 3 in Triangle B could be the similar side to Triangle A's side of 27 or 15 or 21. So the sides of A could be #27/3# of B, or #15/3# of B, or #21/3# of B. So let's run through all the possibilities:

#27/3# or 9 times smaller: #27/9 = 3, 15/9 = 5/3, 21/9 = 7/3#

#15/3# or 5 times smaller: #27/5, 15/5 = 3, 21/5#

#21/3# or 7 times smaller: #27/7, 15/7, 21/7 = 3#