Final answer:
The length of side AB is 15.8 units.
Step-by-step explanation:
The length of side AB can be found by using the information provided. Since the length of side AB is twice the length of side AC, we can represent side AB as 2x. The perimeter of a triangle is calculated by adding the lengths of all three sides. So, the expression for the perimeter of the triangle would be: 2x + (5x-1) + 3x. Simplifying this expression by combining like terms, we get: 10x - 1. We are given that the perimeter of the triangle is 78 units, so we can set up the equation 10x - 1 = 78 and solve for x. Adding 1 to both sides, we get 10x = 79. Dividing both sides by 10, we find that x = 7.9. Since side AB is twice the length of side AC, the length of side AB would be 2 times x, which is 2 times 7.9, or 15.8 units.