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

Answer:

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

Step-by-step 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