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?

1 Answer
smendyka
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 * 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#

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