Final answer:
The problem involves determining the shortest side of a triangle with a given perimeter and specific relationships between the sides. By setting up an equation based on the given conditions, we can find that the shortest side of the triangle is 12 inches long.
Step-by-step explanation:
The question revolves around finding the shortest side of a triangle when given the total perimeter and specific conditions regarding the lengths of the other two sides. Let's denote the first side's length as x inches. According to the problem, the second side is 5 inches longer than twice the first side, which can be represented as 2x + 5 inches. The third side is described as being 4 inches less than three times the first side, or 3x - 4 inches. The perimeter of the triangle is the sum of all its sides, which is given as 73 inches. Therefore, we have the equation:
- x + (2x + 5) + (3x - 4) = 73 inches
Simplifying this equation:
- 6x + 1 = 73 inches
- 6x = 72 inches
- x = 12 inches
Thus, the first side of the triangle, which is the shortest side, is 12 inches long.