Question

The length of a lacrosse field is 15 yards less than twice its width, and the perimeter is 330 yards. The defensive area of the field is 3/20 of the total field area. How do you find the defensive area of the lacrosse field?

Answer 1

The Defensive Area is 945 square yards.

Explanation:

To solve this problem you first need to find the area of the field (a rectangle) which can be expressed as `A = L * W`

To get the Length and Width we need to use the formula for the Perimeter of a Rectangle: `P = 2L + 2W`.

We know the perimeter and we know the relation of the Length to the Width so we can substitute what we know into the formula for the perimeter of a rectangle:
`330 = (2*W) +(2*(2W - 15)` and then solve for `W`:

`330 = 2W + 4W - 30`

`360 = 6W`

`W = 60`

We also know:
`L = 2W - 15` so substituting gives:

`L = 2*60 - 15` or `L = 120 - 15` or `L = 105`

Now that we know the Length and Width we can determine the Total Area:
`A = 105 * 60 = 6300`

`D` or the Defensive Area is:
`D = (3/20) 6300 = 3 * 315 = 945`