Question

A new community Wellness Complex is being built in Madison. The perimeter of the rectangular playing field is 446 yards. The length of the field is 7 yards less than quadruple the width. What are the dimensions of the playing field?

Answer 1

The length of the rectangular playing field is 177 yards and the width is 46 yards

Explanation:

Let

x -----> the length of the rectangular playing field

x -----> the width of the rectangular playing field

we know that

The perimeter of the rectangular playing field is

P=2(x+y)

P=446 yd

so

446=2(x+y) ------> equation A

x=4y-7 -----> equation B

Solve the system by substitution

Substitute equation B in equation A and solve for y

446=2(4y-7+y)

223=5y-7

5y=223+7

5y=230

y=46

Find the value of x

x=4(46)-7

x=177

therefore

The length of the rectangular playing field is 177 yards and the width is 46 yards