Question

Find the dimensions of an American football field. The length is 200 ft more than the width, and the perimeter is 1,040 ft. Find the length and width. Use the perimeter formula

Answer 1

The width of the American football field is 160 feet, and the length is 360 feet, as determined by using the perimeter formula and the given conditions of the problem.

Step-by-step explanation:

The student is asking for help with a mathematics problem involving the dimensions of an American football field. To solve for the length and width of the field, we need to use the perimeter formula for a rectangle, which is Perimeter = 2×(length + width). The problem statement provides two key pieces of information: the length is 200 ft more than the width, and the total perimeter is 1,040 ft.

Let the width be represented by w. Then the length would be w + 200 ft. Plugging these into the perimeter formula, we get 1,040 = 2×(w + (w + 200)). Solving this equation, we find:

1,040 = 2w + 2w + 400
1,040 = 4w + 400
1,040 - 400 = 4w
640 = 4w
w = 160 ft

Now, using the width, we can find the length:

Length = 160 ft + 200 ft = 360 ft

Therefore, the width of the American football field is 160 feet, and the length is 360 feet.

Answer 2

The width of the football field is 160 feet.

The length of the football field is 360 feet.

Step-by-step explanation:

Let w represent width of the football field.

We have been given that the length is 200 ft more than the width, so the length of the field would be
`w+200`.

We are also told that the perimeter is 1,040 ft. We know that football field is in form of rectangle, so perimeter of field would be 1 times the sum of length and width. We can represent this information in an equation as:

`2(w+w+200)=1040`

Let us solve for w.

`2(2w+200)=1040`

`4w+400=1040`

`4w+400-400=1040-400`

`4w=640`

`(4w)/(4)=(640)/(4)`

`w=160`

Therefore, the width of the football field is 160 feet.

Upon substituting
`w=160` in expression
`w+200`, we will get length of field as:

`w+200\Rightarrow 160+200=360`

Therefore, the length of the football field is 360 feet.