Triangle A has sides of lengths #36 ,24 #, and #27 #. Triangle B is similar to triangle A and has a side of length #5 #. What are the possible lengths of the other two sides of triangle B?

1 Answer
Dec 7, 2017

Possible lengths of the triangle B are

Case (1)
#5, 5.625, 7.5#

Case (2)
#5, 4.44, 6.67#

Case (3)
#5, 3.33, 3.75#

Explanation:

Triangles A & B are similar.
Case (1)
#:.5/24=b/27=c/36#
#b=(5*27)/24= 5.625#
#c=(5*36)/24= 7.5#

Possible lengths of other two sides of triangle B are
#5, 5.625, 7.5#

Case (2)
#:.5/27=b/24=c/36#
#b=(5*24)/27=4.44#
#c=(5*36)/27=6.67#

Possible lengths of other two sides of triangle B are
#5, 4.44, 6.67#

Case (3)
#:.5/36=b/24=c/27#
#b=(5*24)/36=3.33#
#c=(5*27)/36=3.75#

Possible lengths of other two sides of triangle B are
#5, 3.33, 3.75#