Triangle A has sides of lengths #42 ,36 #, and #21 #. Triangle B is similar to triangle A and has a side of length #14 #. What are the possible lengths of the other two sides of triangle B?

1 Answer
salamat
Jan 12, 2017

The possible length of sides for triangle B are #{14,12,7}#, #{14,49/3,49/6}#,#{14,28,24}#

Explanation:

Let say 14 is a length of triangle B reflect to the length of 42 for triangle A and X,Y are the length for other two sides of triangle B.

#X/36 = 14/42#
#X=14/42*36#
#X=12#

#Y/21 = 14/42#
#Y=14/42*21#
#Y=7#
The length of sides for triangle B are #{14,12,7}#

Let say 14 is a length of triangle B reflect to the length of 36 for triangle A and X,Y are the length for other two sides of triangle B.
#X/42 = 14/36#
#X=14/36*42#
#X=49/3#

#Y/21 = 14/36#
#Y=14/36*21#
#Y=49/6#
The length of sides for triangle B are #{14,49/3,49/6}#

Let say 14 is a length of triangle B reflect to the length of 21 for triangle A and X,Y are the length for other two sides of triangle B.
#X/42 = 14/21#
#X=14/21*42#
#X=28#

#Y/36 = 14/21#
#Y=14/21*36#
#Y=24#
The length of sides for triangle B are #{14,28,24}#

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