Triangle A has sides of lengths #7 ,4 #, and #8 #. Triangle B is similar to triangle A and has a side of length #9 #. 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)
#9, 15.75, 18#

Case (2)
#9, 5.14, 10.29#

Case (3)
#9, 4.5, 7.875#

Explanation:

Triangles A & B are similar.
Case (1)
#:.9/4=b/7=c/8#
#b=(9*7)/4= 15.75#
#c=(9*8)/4= 18#

Possible lengths of other two sides of triangle B are
#9, 15.75, 18#

Case (2)
#:.9/7=b/4=c/8#
#b=(9*4)/7=5.14#
#c=(9*8)/7=10.29#

Possible lengths of other two sides of triangle B are
#9, 5.14, 10.29#

Case (3)
#:.9/8=b/4=c/7#
#b=(9*4)/8=4.5#
#c=(9*7)/8=7.875#

Possible lengths of other two sides of triangle B are
#9, 4.5, 7.875#