# Triangle A has sides of lengths #36 #, #48 #, 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:

Any of the 3 sides of triangle B could be of length 3 hence there are 3 different possibilities for the sides of B.

Since the triangles are similar then the

#color(blue)"ratios of corresponding sides are equal"# Let the 3 sides of triangle B be a ,b and c, corresponding to the sides 36 ,48 and 18 in triangle A.

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If side a = 3 then ratio of corresponding sides#=3/36=1/12# hence side b

#=48xx1/12=4" and side c" =18xx1/12=3/2# The 3 sides of B would be

#(3,color(red)(4),color(red)(3/2))#

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If side b = 3 then ratio of corresponding sides#3/48=1/16# a

#=36xx1/16=9/4" and side c" =18xx1/16=9/8# The 3 sides of B would be

#=(color(red)(9/4),3,color(red)(9/8))#

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If side c = 3 then ratio of corresponding sides#=3/18=1/6# hence

#a=36xx1/6=6" and b" =48xx1/6=8# The 3 sides of B would be

#=(color(red)(6),color(red)(8),3)#

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