Triangle A has sides of lengths #24 #, #28 #, and #16 #. Triangle B is similar to triangle A and has a side of length #7 #. What are the possible lengths of the other two sides of triangle B?

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Answer 1 · 2017-11-19T11:57:12

Three sets of possible lengths are
1) # 7, 49/6, 14/3#
2) # 7, 6, 4#
3) #7, 21/2, 49/4#

If two triangles are similar, their sides are on the same proportion.
#A/a = B/b = C/c#

Case 1.
#24/7 = 28/b = 16/c#
#b = (28*7)/24 = 49/6#
#c = (16*7)/24 = 14/3#

Case 2.
#28/7 = 24/b = 16/c#
#b = 6, c = 4#

Case 3.
#16/7 =24/b = 28/c#
#b 21/2, c = 49/4#