Question

The perimeter of a soccer field is 320 feet. The length of the field is 20 less than twice the width. Find the dimensions of the soccer field. Let l represent the length of the field and w the width. A. One equation in the system comes from the fact that the perimeter of the field is 320 feet. Equation is:

B. The other equation comes from the fact that the length is 20 less than twice the width. Equation is: C. Solve the system.
The length of the field is:
And the width is:

Answer 1

Answer: The length of the field is 100 feet and the width is 60 feet.

Step-by-step explanation:

a. The perimeter of a rectangle is the sum of the lengths of all its sides. For a soccer field, the perimeter is the sum of the lengths of two adjacent sides, which are equal in length, and the sum of the lengths of the other two adjacent sides, which are also equal in length. Therefore, we can write the equation:

2l + 2w = 320

b. According to the problem, the length of the field is 20 less than twice the width. In equation form, this is:

l = 2w - 20

c. To solve the system of equations, we can substitute the expression for l from equation b into equation a, and then solve for w:

2(2w - 20) + 2w = 320

Simplifying:

4w - 40 + 2w = 320

6w - 40 = 320

6w = 360

w = 60

Now that we know the width is 60 feet, we can substitute this value into equation b to find the length:

l = 2w - 20

l = 2(60) - 20

l = 100

Therefore, the length of the field is 100 feet and the width is 60 feet.

Answer 2

The perimeter of the soccer field is 320 feet and the length is 20 less than twice the width. The dimensions of the soccer field are 100 feet for the length and 60 feet for the width.

Step-by-step explanation:

A. The perimeter of the field is given as 320 feet. The perimeter of a rectangle is equal to the sum of all its sides. Thus, for a rectangle with length l and width w, the perimeter would be 2l + 2w. Since the perimeter is given as 320 feet, we can set up the equation: 2l + 2w = 320.

B. The length of the field is 20 less than twice the width. This can be expressed as l = 2w - 20.

C. To solve the system of equations, we can substitute the value of l from equation B into equation A: 2(2w - 20) + 2w = 320. Simplifying, we get 4w - 40 + 2w = 320, which gives us 6w - 40 = 320. Solving for w, we have 6w = 360, and w = 60. Substituting this value back into equation B, we find l = 2(60) - 20 = 100.

Therefore, the dimensions of the soccer field are 100 feet for the length and 60 feet for the width.