Backyard garden rectangular in shape. determine the best length and width(in feet). how many feet of fencing would be needed? use the formula p=2l+2w

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 - 2W2

Let area be y, so y = -2W2 +42W

Note this is a parabola pointing down because the coefficient of the W2 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 aW2 + bW + c = 0

a = -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 ft2