Triangle A has sides of lengths #27 #, #12 #, 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
Dec 7, 2017

Possible lengths of the triangle B are

Case (1)
#3, 5.25, 6.75#

Case (2)
#3, 1.7, 3.86#

Case (3)
#3, 1.33, 2.33#

Explanation:

Triangles A & B are similar.
Case (1)
#:.3/12=b/21=c/27#
#b=(3*21)/12= 5.25#
#c=(3*27)/12= 6.75#

Possible lengths of other two sides of triangle B are
#3, 5.25, 7.75#

Case (2)
#:.3/21=b/12=c/27#
#b=(3*12)/21=1.7#
#c=(3*27)/21=3.86#

Possible lengths of other two sides of triangle B are
#3, 1.7, 3.86#

Case (3)
#:.3/27=b/12=c/21#
#b=(3*12)/27=1.33#
#c=(3*21)/27=2.33#

Possible lengths of other two sides of triangle B are
#3, 1.33, 2.33#