Triangle A has sides of lengths #54 #, #44 #, and #32 #. Triangle B is similar to triangle A and has a side of length #4 #. What are the possible lengths of the other two sides of triangle B?

Question

Triangle A has sides of lengths #54    #, #44    #, and #32     #. Triangle B is similar to triangle A and has a side of length #4     #. What are the possible lengths of the other two sides of triangle B?

Sadie Adams · Accepted Answer

Because the problem doesn't state which side in Triangle A corresponds to the side of length 4 in triangle B, there are multiple answers. If the side with length 54 in A corresponds to 4 in B: Find the proportionality constant: #54K=4# 
#K =4/54=2/27# The 2nd side #=2/27 *44=88/27#
The3rd side#=2/27*32=64/27# If the side with length 44 in A corresponds to 4 in B: #44K=4#
#K=4/44 = 1/11# The 2nd side#=1/11*32=32/11#
The 3rd side#=1/11*54=54/11# If the side with length 32 in A corresponds to 4 in B: #32K=4#
#K=1/8# The 2nd side#=1/8 *44=11/2#
The 3rd side#=1/8*54=27/4#

James Atkins · Answer

undefined The possible lengths of the other two sides of triangle B are $ \frac{4}{54} \times 44 $ and $ \frac{4}{54} \times 32 $, which simplify to approximately $ \frac{16}{3} $ and $ \frac{64}{9} $, respectively.

Sophia Alfred · Answer

undefined The ratio of corresponding sides of similar triangles is the same. Let the sides of triangle B be $ x $ and $ y $. The ratio of the sides of triangle B to triangle A is $ \frac{x}{54} = \frac{y}{44} = \frac{4}{32} $.

From this, we can find that $ x = \frac{54}{32} \cdot 4 $ and $ y = \frac{44}{32} \cdot 4 $.

Simplifying, we get $ x = \frac{27}{2} $ and $ y = 11 $.

Therefore, the possible lengths of the other two sides of triangle B are $ \frac{27}{2} $ and 11.