SOLUTION: the length of a triangle are 5,12 and 13 what is the length of the longest side of a similar triangle whose perimeter is 90

Question 515883: the length of a triangle are 5,12 and 13 what is the length of the longest side of a similar triangle whose perimeter is 90
Found 2 solutions by Alan3354, drcole:
Answer by Alan3354(69443) (Show Source): You can put this solution on YOUR website!
That's 3 times the perimeter of the 5, 12, 13 triangle, so it's 3*13 = 39.
Answer by drcole(72) (Show Source): You can put this solution on YOUR website!
If a triangle has sides of length 5, 12, and 13, a similar triangle will have sides of length 5x, 12x, and 13x, where x is some positive number. This is because with a similar triangle, all of the lengths will be multiplied by the same number. The perimeter of this new triangle is then:
5x + 12x + 13x = 30x
We know that this new perimeter is 90, so we have an equation, which we can solve for x:
30x = 90
x = 3
So all of the side lengths are multiplied by 3. Therefore the longest side of the new triangle is 13(3) = 39.
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