Final answer:
The lengths of the sides of the triangular sail are found by setting up equations with the relationships between the sides. After solving, the sides are determined to be a = 25 ft, b = 14 ft, and c = 18 ft.
Step-by-step explanation:
The problem given is solving for the lengths of the sides of a triangle when we know the perimeter and the relationships between the sides. By setting up equations based on the provided relations and the perimeter, we can find the length of each side.
Let's call the length of side b 'b'. According to the problem, side a is 3 ft shorter than twice side b (a = 2b - 3) and side c is 4 ft longer than side b (c = b + 4). The perimeter of the triangle is the sum of its sides, which is given as 57 ft. Therefore:
- a + b + c = 57
- 2b - 3 + b + b + 4 = 57
- 4b + 1 = 57
- 4b = 56
- b = 14
Now that we have the length of side b, we can calculate sides a and c:
- a = 2b - 3 = 2(14) - 3 = 25
- c = b + 4 = 14 + 4 = 18
Therefore, the lengths of the sides are a = 25 ft, b = 14 ft, and c = 18 ft.