Question

A rectangular garden is to be constructed using a rock wall as one side and fencing for the other three sides. There are 28 yards of fencing available. Determine the dimensions that would create the garden of maximum area. What is the maximum area? Enter only the maximum area. Do not include units in your answer.

Answer 1

Answer:

Maximum area = 98

Step-by-step explanation:

Fencing available = 28 yards

Let l be the length and w be the width of rectangular garden,

We have fencing in 3 sides 3 sides

That is

         Fencing needed = 2l + w = 28

                                        w = 28 - 2l

          Area of rectangle = l x w = l x (28 -2l) = 28l-2l²

For maximum area we have,

                   $\frac{dA}{dl}=0\\\\\frac{d}{dl}\left ( 28l-2l^2\right )=0\\\\28-4l=0\\\\l=7yards$

We have

                     2l + w = 28

                    2 x 7 + w = 28

                     w = 14 yards

Maximum area = 7 x 14 = 98 yard²

Maximum area = 98