Triangle A has sides of lengths #32 #, #48 #, and #36 #. Triangle B is similar to triangle A and has a side of length #8 #. What are the possible lengths of the other two sides of triangle B?

2 Answers
Oct 18, 2017

The other two sides are 12, 9 respectively.

Explanation:

Since the two triangles are similar, corresponding sides are in the same proportion.
If the #Delta#s are ABC & DEF,
#(AB)/(DE) =( BC)/(EF) = (CA)/(FD)#

#32/8 = 48/(EF) = 36 / (FD)#
#EF = ( 48 * 8)/32 = 12#
#FD = (36 * 8)/ 32 = 9#

Oct 18, 2017

The other two sides of triangle #B# could have lengths:

#12# and #9#

#16/3# and #6#

#64/9# and #96/9#

Explanation:

Given triangle A has sides of lengths:

#32, 48, 36#

We can divide all these lengths by #4# to get:

#8, 12, 9#

or by #6# to get:

#16/3, 8, 6#

or by #9/2# to get:

#64/9, 96/9, 8#

So the other two sides of triangle #B# could have lengths:

#12# and #9#

#16/3# and #6#

#64/9# and #96/9#