Question

The perimeter of a football field is 920 feet. The width is 60 feet more than one-third of the length. What are the dimensions of a football field?

Answer 1

Given:

Perimeter of a football field = 920 feet.

The width is 60 feet more than one-third of the length.

To find:

The dimensions of a football field.

Solution:

Let the length of the field be x.

Then, width =
`(1)/(3)x+60`

We know that,

`Perimeter = 2( length + width)`

`920 = 2(x+(1)/(3)x+60)`

`920 = 2((4)/(3)x+60)`

`920 =(8)/(3)x+120`

Subtract both sides by 120.

`920-120 =(8)/(3)x+120-120`

`800 =(8)/(3)x`

Multiply both sides by 3.

`2400 =8x`

Divide both sides by 8.

`300 =x`

Now,

`Length = 300\text{ feet}`

`Width=(1)/(3)(300)+60`

`Width=100+60`

`Width=160\text{ feet}`

Therefore, the length and width of the football field are 300 feet and 160 feet respectively.