# 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 triangle?

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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.

The ratio of sides of the first triangle is 9:15:18.

The ratio of sides of the similar triangle is 6:X:Y.

Now, we'll determine the proportion:

6/9 = a

We'll cross multiply and we'll get:

9a = 6

We'll divide by 3:

3a = 2

a = 2/3

We'll multiply each known length of the side by the proportion a:

9*(2/3) = 6

15*(2/3) = 10

18*(2/3) = 12

**The length of the longest side of the triangle is of 12 units.**