a farmer has two rectangular gardens from 200 yards of fencing, they are planted beside each other so they share a side.

Question

two rectangular gardens are made from 200 yards of fencing. the gardens are planted beside each other so they share a side. If the farmer wants the total area to be as large as possible, what dimensions should he make the gardens? what will the largest possible area be?

Answer 1

    _______________________________

    ¦                  ¦                          ¦

    ¦                  ¦                          ¦y

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                        x

 3y + 2x = 200

Area = xy

The maximum area is obtained by dividing the 200 yards equally between the X sides and the Y sides.

This means that  3y = 100  ⇒ y = 100/3 = 33.33 yards

                         2x = 100  ⇒ x = 100/2  = 50 yards

Maximum area = xy = 50(33.33) =1666.67 square yards