A new Outdoor recreation Center is being built in Erie. The perimeter of the rectangular playing field is 456 yards. The length of the field is 7 yards less than quadruple the width. What are the dimensiA new Outdoor Recreation ons of the playing field?

   (1)

And for this case we know the following condition "The length of the field is 7 yards less than quadruple the width" and we can write this :

And replacing into equation (1) we got:

Adding 14 in both sides we got:

And dividing 10 on both sides we got:

And then we can solve for X and we got:

Step-by-step explanation:

For this case we can set up the following notation:

X represent the lenght

Y represent the width

And since we have a rectangular playing filed the perimeter is given by:

   (1)

And for this case we know the following condition "The length of the field is 7 yards less than quadruple the width" and we can write this :

And replacing into equation (1) we got:

Adding 14 in both sides we got:

And dividing 10 on both sides we got:

And then we can solve for X and we got: