A triangle has sides that are of unknown lengths but if one side is 4X than the other sites are 10x and 12x. It's perimeter is 104 inches. Determine the length of each side so the steps of your answer clearly check your answer and then state your answer clearly.

the perimeter is the sum of the 3 sides of the triangle, hence

4x + 10x + 12x = 104

26x = 104 (divide both sides by 26)

x = 4

thus the sides of the triangle are

4x = 4 * 4 = 16 inches

10x = 10 * 4 = 40 inches

12x = 12 * 4 = 48 inches

As a check

16 + 40 + 48 = 104 inches ← correct