The "4" ranch is 7680 acres. It is a rectangle that is a mile longer than it is wide. What are the dimensions of the ranch?

Answer 1

let's work in feet (hate this non-metric stuff)

1 mile = 5280 ft

let the width be x
then the length is x+5280

area = x(x+5280)

1 acre = 43560 ft^2
then 7680 acres = 334540800 ft^2

x^2 + 5280x = 334540800
complete the square ...
x^2 + 5280x + 6969600 = 334540800+6969600
(x+264)^2 = 341510400
x + 264 = ±18480
x = 18216 or x is a negative, which would be silly

so the ranch is 18216 ft by 23496 ft
or 3.45 miles by 4.45 miles

(would have been so easy in metric)