If you enclose a rectangle garden using a side of a building as one side of the rectangle, what are the dimensions of the garden if it is to be the maximum area that you can enclose with 42 feet of the fence?

L = building side

W = non-building side

P = 2W + L = 42 (note only one L because the other L is the building itself)

Solve for L:

L = 42 - 2W

Area = l*w

Area = (42-2W)W = 42W - 2W

^{2}Let area be y, so y = -2W

^{2}+42WNote this is a parabola pointing down because the coefficient of the W

^{2 }is negative. That makes the vertex the maximum for which we are searching.Vertex of this parabola is at W=-b/2a, if the quadratic is aW

^{2}+ bW + c = 0a = -2

b = 42

W = -42/(2*-2) = -42/-4 = 10.5

W = 10.5

L = 42-2(10.5) = 42-21 = 21

Area = L*W = 21 * 10.5

A = 220.5 ft

^{2}
## Comments

^{2}, basically. The UNITS are square feet.^{2}and mine was 220.5 sq feet. same thing.... my brain is fried from doing math all day. Sorry and thank you for your help. lol