Question

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

between 100 and 130 yards. One particular soccer field has a perimeter of 320 yards. Its
length measures 40 yards more than its width. What are the dimensions of this field?

The length is___yards.

The width is____yards.

Answer 1

`perimeter = 2(l + w) \\ but \: length = 40 * width \\ perimeter = 2(40w + w) \\ p = 2(41w) \\ 320 = 2(41w) \\ w = (320)/((2 * 41)) \\ w = 3.902 \: yards \\ length = 40 * w \\ = 40 * 3.902 \\ l = 156.08 \: yards`

Answer 2

9514 1404 393

Answer:

• length: 100 yards
• width: 60 yards

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.