The perimeter of the rectangular play field is 380 yards. The length of the field is 6 yards less than triple the width.

Question

A new neighborhood Activity Complex is being built in Erie. The perimeter of the rectangular play field is 380 yards. The length of the field is 6 yards less than triple the width. What are the dimensions of the playing field?

 

need to know the width and length in yards

 

Answer 1

You know the formula for perimeter of a rectangle is 2(L+W):

That's in 2 variables, but the formula for length is expressed in terms of width.

You know the formula for Length is 3*W - 6yds ; where W is the width

Now you have an equation in terms of one variable:

 

Plug in the values for the known, and solve for the unknown:

 

380 yds = 2((3*W - 6 yds) + W)

380 yds = 2(3W - 6 yds + W)

380 yds = 2(4W - 6 yds)

380 yds = 8W - 12 yds

380 yds + 12 yds = 8W

392 yds = 8W

392 yds/8 = W

49 yds = W

 

Now for the Length:

L = 3*(49 yds) - 6 yds

L = 147 yds - 6 yds

L = 141 yds

 

To Check:

P = 2(141 yds + 49 yds)

P = 2(190 yds)

P = 380 yds   ; check