# 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?

Oct 27, 2016

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 $A = L \cdot W$

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

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 $W$:

$330 = 2 W + 4 W - 30$

$360 = 6 W$

$W = 60$

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

$L = 2 \cdot 60 - 15$ or $L = 120 - 15$ or $L = 105$

Now that we know the Length and Width we can determine the Total Area:
$A = 105 \cdot 60 = 6300$

$D$ or the Defensive Area is:
$D = \left(\frac{3}{20}\right) 6300 = 3 \cdot 315 = 945$