Afarmer decides to enclose a rectangular garden, using the side of a barn as one side of the rectangle. what is the maximum area that the farmer can enclose with 100 ft of fence? what should the dimensions of the garden be to give this area?

The perimeter will be:
 P = 2x + y
 100 = 2x + y
 The area is:
 A = x * y
 We write the area as a function of x:
 A (x) = x * (100-2x)
 Rewriting:
 A (x) = 100x - 2x ^ 2
 We derive:
 A '(x) = 100 - 4x
 We equal zero and clear x:
 0 = 100 - 4x
 4x = 100
 x = 25 feet
 The other dimension is:
 y = 100-2x
 y = 100-2 (25)
 y = 100-50
 y = 50 feet
 The area will be:
 A = (25) * (50)
 A = 1250 feet ^ 2
 
 the maximum area that the farmer can enclose with 100 ft of fence is:
 A = 1250 feet ^ 2
 The dimensions of the garden to give this area should be:
 x = 25 feet
 y = 50 feet

Distance=slopeslope is -2/4which equals-1/2the distance between these two points is -1/2