let

l = the length of the field

w = the width of the field

P = 2(l + w) the perimeter of the field

A person jogged 10 times along the perimeter of a rectangular field at the rate of 12 kilometers per hour for 30 minutes:

10P = 12*0.5 (since 30 min = 0.5 hr)

10P = 6

10*2(l + w) = 6

20(l + w) = 6 divide both sides by 2

10(l + w) = 3

the field has a length that is twice as long as it's width: l = 2w

plug l = 2w into 10(l + w) = 3

10(2w+ w) = 3

w = 3/30

w = 1/10 km = 100 m

l = 2/10 km = 200 m

the area A = l*w

A = 200*100

A = 20,000 m^2 is the area of the field.