Question

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?

Answer 1

`P= 456 = 2X +2Y` (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 :

`X = 4Y -7`

And replacing into equation (1) we got:

`456= 2(4Y-7) +2Y`

`456 = 8Y -14 +2Y`

`456 = 10Y-14`

Adding 14 in both sides we got:

`456+14 = 10Y`

And dividing 10 on both sides we got:

`Y=(470)/(10)= 47`

And then we can solve for X and we got:

`X= 4*47 -7=181`

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:

`P= 456 = 2X +2Y` (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 :

`X = 4Y -7`

And replacing into equation (1) we got:

`456= 2(4Y-7) +2Y`

`456 = 8Y -14 +2Y`

`456 = 10Y-14`

Adding 14 in both sides we got:

`456+14 = 10Y`

And dividing 10 on both sides we got:

`Y=(470)/(10)= 47`

And then we can solve for X and we got:

`X= 4*47 -7=181`