A farmer wishes to enclose a rectangular garden with 300 yar

A farmer wishes to enclose a rectangular garden with 300 yards fencing. A river runs along one side of the garden, so no fencing is needed there. If the side opposite the river runs twice as long as the other two sides, what are the dimensions of the field?

Solution

Let the side opposite to the river be x. Then each of thesides perpendicular to this side is x/2. Since the fencing admeasuring 300 yards suffices for 3 sides excepting the side facing the river ( for which, no fencing is required), we have x + x/2 + x/2 = 300 or, 2x = 300 or, x = 150 yards. Then x/2 = 75 yards and the dimensions of the rectangular field are 150 yards by 75 yards.