Triangle A has sides of lengths #15 #, #12 #, and #18 #. Triangle B is similar to triangle A and has a side of length #3 #. What are the possible lengths of the other two sides of triangle B?
1 Answer
Explanation:
Since triangle B has 3 sides, anyone of them could be of length 3 and so there are 3 different possibilities.
Since the triangles are similar then the ratios of corresponding sides are equal.
Name the 3 sides of triangle B , a, b and c corresponding to the sides 15 , 12 and 18 in triangle A.
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If side a = 3 then the ratio of corresponding sides#=3/15=1/5# hence b
#=12xx1/5=12/5" and " c=18xx1/5=18/5# The 3 sides of B
#=(3,12/5,18/5)#
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If side b = 3 then the ratio of corresponding sides#=3/12=1/4# hence a
#=15xx1/4=15/4" and "c=18xx1/4=9/2# The 3 sides of B
#=(15/4,3,9/2)#
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If side c = 3 then the ratio of corresponding sides#=3/18=1/6# hence a
#=15xx1/6=5/2" and "b=12xx1/6=2# The 3 sides of B
#=(5/2,2,3)#
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