Answer:Step-by-step explanation:Let the length of the fence = x
Let the width of the fence = y
Recall that the perimeter of a rectangle is calculated by 2(L+B) , but the farmer is using the side of the barn on one side of the rectangle , so the perimeter equation is x + 2y = 48 Area = xy
If we substitute the perimeter equation so that the area is only in terms of y.
Area = (48 - 2y)y
Area = 48y - 2[tex]y^{2}[/tex] Now just find the vertex of the parabola
Area = -2 [tex]y^{2}[/tex]+ 48y
A = -2 [tex]y^{2}[/tex] + 48Differentiate A with respect to y[tex]\frac{dA}{dy}[/tex] = -4y + 48equate it to zero , we have -4y + 48 = 04y = 48 y = 12Substitute y = 12 into equation 1, we havex = 48 - 2yx = 48 - 2(12)x = 48 - 24x = 24Therefore the dimensions of the garden are 24 by 12The maximum area is 288 square unit