Triangle A has sides of lengths #12 ,17 #, and #11 #. 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?

Question

Triangle A has sides of lengths #12     ,17   #, and #11     #. 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?

Mason Adams · Accepted Answer

Possible lengths of the triangle B are

Case (1)
#9, 8.25, 12.75#

Case (2)
#9, 6.35, 5.82#

Case (3)
#9, 9.82, 13.91# Triangles A & B are similar. Case (1) #:.9/12=b/11=c/17# #b=(9*11)/12= 8.25# #c=(9*17)/12= 12.75 Possible lengths of other two sides of triangle B are #9, 8.25, 12.75# Case (2) #:.9/17=b/12=c/11# #b=(9*12)/17=6.35# #c=(9*11)/17=5.82# Possible lengths of other two sides of triangle B are #9, 6.35, 5.82# Case (3) #:.9/11=b/12=c/17# #b=(9*12)/11=9.82# #c=(9*17)/11=13.91# Possible lengths of other two sides of triangle B are #9, 9.82, 13.91#

Noah Atkinson · Answer

undefined Using the properties of similar triangles, we can set up a proportion between corresponding sides of Triangle A and Triangle B.

Let the lengths of the sides of Triangle B be $ x $ and $ y $. Then the proportion between corresponding sides of Triangle A and Triangle B is:

$$ \frac{x}{12} = \frac{9}{17} $$

Solving for $ x $, we get:

$$ x = \frac{9 \times 12}{17} = \frac{108}{17} $$

Similarly, setting up another proportion:

$$ \frac{y}{17} = \frac{9}{11} $$

Solving for $ y $, we get:

$$ y = \frac{9 \times 17}{11} = \frac{153}{11} $$

Therefore, the possible lengths of the other two sides of Triangle B are $ \frac{108}{17} $ and $ \frac{153}{11} $.