Final answer:
To find the length of each side of the pasture, a 455-foot fence is considered. An equation is formed with the expressions for the sides, and solving it, we find that x equals 50 feet. Hence, the side lengths in ascending order are 50 feet, 75 feet, 150 feet, and 180 feet.
Step-by-step explanation:
The student is asking for the length of each side of a four-sided pasture that is surrounded by a 455-foot fence. We know the lengths of three sides are represented by 3x feet, 1.5x feet, and x feet, and the fourth side is 180 feet. To find the values of x, we need to set up an equation 3x + 1.5x + x + 180 = 455, which represents the total length of the fence. Solving this equation, we combine like terms to get 5.5x + 180 = 455. Subtracting 180 from both sides gives us 5.5x = 275, and dividing both sides by 5.5 gives us x = 50 feet. Therefore, the side lengths in order from least to greatest are 50 feet, 75 feet (1.5x), 150 feet (3x), and 180 feet.