If the sides of a triangle measure 8,9,and 10 find the longest side of a similar triangle whose perimeter is 81.

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The perimeter of the triangle whose dimensions we know is 27. Therefore, the proportion of each side of the two triangles must be 81:27 which happens to be 3:1.

To find the longest side of the second triangle, we set up the following equation:

3/1 = x/10

Now we cross multiply to find for x.

x = 30

This makes sense because the second triangle is 3 times the size of the first so each side of the second triangle must be 3 times the length of the corresponding side on the first triangle.

**So, the longest side of the second triangle is 30 units long.**

First,we'll calculate the perimeter of the original triangle, adding up the three lengths of the sides:

P1 = 8+9+10

P1 = 27

Now, we'll divide the perimeter of the similar triangle, namely 81, by the perimeter of the original triangle:

P2 = 81

P2/P1 = 81/27

P2/P1 = 3 units

So, the rapport is of 3 units. We'll multiply the length of each side of the original triangle by 3:

8*3 = 24 units

9*3 = 27 units

10*3 = 30 units

The longest length of the side of the similar triangle is of 30 units.

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