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 = $\dfrac{1}{3}x+60$

We know that,

$Perimeter = 2( length + width)$

$920 = 2(x+\dfrac{1}{3}x+60)$

$920 = 2(\dfrac{4}{3}x+60)$

$920 =\dfrac{8}{3}x+120$

Subtract both sides by 120.

$920-120 =\dfrac{8}{3}x+120-120$

$800 =\dfrac{8}{3}x$

Multiply both sides by 3.

$2400 =8x$

Divide both sides by 8.

$300 =x$

Now,

$Length = 300\text{ feet}$

$Width=\dfrac{1}{3}(300)+60$

$Width=100+60$

$Width=160\text{ feet}$

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