Question

A rectangular soccer field may have a width between 50 and 100 yards and a length

Answer 1

9514 1404 393

Answer:

• length: 100 yards
• width: 60 yards

Step-by-step explanation:

Let w represent the width of the field. Then the length is (w+40), and the perimeter is ...

  P = 2(L +W)

  320 = 2((w+40) +w) . . . . fill in values

  160 = 2W +40 . . . . . . . . . divide by 2, collect terms

  80 = w +20 . . . . . . . . . . .  divide by 2

  60 = w . . . . . . . . subtract 20

  w+40 = 100

The length is 100 yards; the width is 60 yards.

Answer 2

Answer:

$perimeter = 2(l + w) \\ but \: length = 40 \times width \\ perimeter = 2(40w + w) \\ p = 2(41w) \\ 320 = 2(41w) \\ w = \frac{320}{(2 \times 41)} \\ w = 3.902 \: yards \\ length = 40 \times w \\ = 40 \times 3.902 \\ l = 156.08 \: yards$