Question

A 455-foot fence encloses a pasture. What is the length of each side of the pasture? The shape of the pasture is a trapezoid (sort of).

One side says 3x ft, one side says 1.5x ft, one side says 180ft, and the last side says x ft. How do I solve this problem?

Answer 1

To solve for the lengths of the sides of the pasture, we can set up an equation by adding up the lengths of all four sides and equating it to the total length of the fence. By solving the equation, we find that the lengths of the four sides are approximately 3(42.3077) ft, 1.5(42.3077) ft, 180 ft, and 42.3077 ft.

Step-by-step explanation:

To solve this problem, we need to set up an equation by adding up the lengths of all four sides of the pasture and equating it to the total length of the fence. Let's use the given information:

• One side: 3x ft
• One side: 1.5x ft
• One side: 180 ft
• One side: x ft

We can write the equation as: 3x + 1.5x + 180 + x = 455. Now, we can solve for x.

Combining like terms on the left side of the equation gives us: 5.5x + 180 + x = 455.

Combining like terms on the right side of the equation gives us: 6.5x + 180 = 455.

Next, we can subtract 180 from both sides of the equation: 6.5x = 275.

Finally, we can divide both sides of the equation by 6.5 to solve for x: x = 42.3077.

Therefore, the lengths of the four sides of the pasture are approximately 3(42.3077) ft, 1.5(42.3077) ft, 180 ft, and 42.3077 ft.