Question

Chandra is building a 5,280 foot fence around her property. Her property is the shape of a rectangle. The length of the property is three times the width of the property.

a. Write an equation that can be used to find the length and width of the property. Explain how you came up with your equation,

b. Find the length and width of the property. Justify your answer, using the conditions given in the problem.

Answer 1

a. Let's denote the width of the property as "w". According to the problem, the length of the property is three times the width, so we can represent the length as "3w".

To find the equation that can be used to solve for the length and width, we can use the formula for the perimeter of a rectangle:

Perimeter = 2(length + width)

Since we know the perimeter (5,280 feet), and we have expressions for the length and width, we can substitute these values into the formula and solve for the variables:

2(3w + w) = 5,280

2(4w) = 5,280

8w = 5,280

w = 660

Therefore, the width of the property is 660 feet, and the length is 3 times the width, or 1,980 feet.

b. To check that these values are correct, we can substitute them back into the formula for perimeter and make sure it equals 5,280:

2(1,980 + 660) = 5,280

This is true, so we can be confident that the width of the property is 660 feet and the length is 1,980 feet.