The sides of a triangle are in the ratio 5:12:13. What is the length of each side of the triangle if the perimeter of the triangle is 15 in?

Let a side have ratio value 5.

Let b side have ratio value 12.
Let c side have ratio value 13.
add the ratios of the sides:
5 + 12 + 13 = T

It is given that the perimeter (all sides added) is 15 inches. The length of each side has the same relationship to its ratio as the perimeter does to the ratio total.
a/5 = 15/T
b/12 = 15/T
c/13 = 15/T

To find the length of each side of the triangle, we first need to find the value of the common ratio that relates the sides of the triangle.

Given that the sides are in the ratio 5:12:13, we can set up the equation:

5x + 12x + 13x = 15

where x is the common ratio.

Simplifying the equation gives us:

30x = 15

Dividing both sides by 30 gives us:

x = 15/30

x = 1/2

Now that we know the value of x, we can find the length of each side of the triangle by multiplying x with the respective ratios.

Length of the first side: 5 * (1/2) = 2.5
Length of the second side: 12 * (1/2) = 6
Length of the third side: 13 * (1/2) = 6.5

Therefore, the lengths of each side of the triangle are 2.5, 6, and 6.5 inches.