Question 726768: Each angle of abc sides 3, 6, 4 has the same measure as an angle in xyz (not shown). If the length of one side of xyz is 24, what is one possible perimeter of xyz?
Answer by KMST(5328)   (Show Source):
You can put this solution on YOUR website! If the lengths of the sides of triangle ABC are 3, 6, and 4 (in whatever units),
ABC has a perimeter of  (measured in the same units).
If the angles of triangle XYZ have the same measures as the angles in ABC,
the triangles are similar, meaning that one is a scaled-up version of the other.
If the length of one side of XYZ is 24, XYZ is a larger, scaled-up version of ABC.
We just do not know the scale-up factor, but there are three possibilities.
If the side measuring 24 is the longest, corresponding the the side measuring 6 in ABC,
the scale-up factor is  and everything in XYZ is 4 times longer than in ABC, including the perimeter.
That means the perimeter of XYZ is
If the side measuring 24 is the medium length one,=, corresponding the the side measuring 4 in ABC,
the scale-up factor is  and everything in XYZ is 6 times longer than in ABC, including the perimeter.
That means the perimeter of XYZ is
If the side measuring 24 is the shortest, corresponding the the side measuring 3 in ABC,
the scale-up factor is  and everything in XYZ is 8 times longer than in ABC, including the perimeter.
That means the perimeter of XYZ is
SO the perimeter of XYZ could be  , or  , or 
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