Final answer:
To find the length of each side of the triangle, establish a system of equations based on the given information. Solve the equations to find the shortest side (15.6 cm), then use it to determine the lengths of the other two sides (14.6 cm and 27.2 cm).
Step-by-step explanation:
To solve this problem, let's start by letting the shortest side of the triangle be x cm. According to the question, twice the shortest side is 4 cm less than the longest side. So we can express the longest side as 2x - 4 cm. Given that the longest side is also 5 cm less than the sum of the other two sides, we can represent the middle side as y cm. The longest side thus can also be represented as (x + y) - 5 cm. The perimeter of the triangle is the sum of its sides, given as 73 cm.
We can establish a system of equations based on the information provided:
1. x + y + (2x - 4) = 73
2. 2x - 4 = (x + y) - 5
From equation 2, we can find that y = x - 1. Substituting this into equation 1, we get:
2x + (x - 1) + (2x - 4) = 73
5x - 5 = 73
x = 78 / 5
x = 15.6 cm
Now that we have the value for x, we can find y:
y = 15.6 - 1
y = 14.6 cm
The longest side is 2x - 4:
2(15.6) - 4 = 31.2 - 4
The longest side = 27.2 cm
Therefore, the lengths of the sides of the triangle are 15.6 cm (shortest), 14.6 cm (middle), and 27.2 cm (longest).