Question

A new neighborhood activity complex is being built in erie. The perimeter of the rectangular playing field is 256 yards. The length of the field is 4 yards less than double the width. What are the dimensions of the playing field?

Answer 1

The length of the rectangular playing field is 84 yards and the width is 44 yards

Explanation:

Let

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

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

we know that

The perimeter of the rectangular playing field is equal to

`P=2(x+y)`

`P=256\ yd`

so

`256=2(x+y)` ------> equation A

we have that

`x=2y-4` -----> equation B

Solve the system by substitution

Substitute equation B in equation A and solve for y

`256=2(2y-4+y)`

`128=3y-4`

`3y=128+4`

`3y=132`

`y=44`

Find the value of x

`x=2(44)-4=84`

therefore

The length of the rectangular playing field is 84 yards and the width is 44 yards