# Triangle A has sides of lengths #15 #, #12 #, and #12 #. Triangle B is similar to triangle A and has a side of length #24 #. What are the possible lengths of the other two sides of triangle B?

##### 1 Answer

#### Explanation:

Since the triangles are similar the 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 12 in triangle A.

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If side a = 24 then ratio of corresponding sides# = 24/15 = 8/5 #

hence b = c#= 12xx8/5 = 96/5 #

The 3 sides in B# = (24,96/5,96/5 )#

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If b = 24 then ratio of corresponding sides#= 24/12 = 2#

hence a#= 15xx2 = 30 " and c = 2xx12 = 24 # The 3 sides of B = (30,24,24)

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If c = 24 will give the same result as b = 24