The sides of a triangle measure 9, 15, and 18.If the shortest side of a similar triangle measures 6, find the length of the longest side of this...

Two triangle are simila if the all the three angles of one
triangle are respectively equal to the angles of the other triangle. Or the ratio of the
correspoding sides of the two triangles are equal.

 9,15 and 18 are
the sides of the one triangle and the shortest side of the similar triangle is
6.

So the shortest sides of two triangles 9 and 6 are the
corresponding sides. So Let 6< x < y . Where x and y are the correspondingsides to
15 and 18 respectvely.

So by the ratio property of similar
triangles,

9/6 = 15/x =
18/y....(1)

Therefore 9/6 = 15/x .

Or
9x = 6*15.

So x= 6*15/9 = 10

Also from
(1) , 9/6 = 18/y.

So 9y = 6*18.

y =
6*18/9 = 12.

Therefore the sides of the similar triangle are 6, 10,
12.