Asked by Godstar
A rectangular fence is to be made and the available bar wire is 60cm, what are the dimensions of the rectangular closure that will give the maximum area, what is the maximum area?
Answers
Answered by
Reiny
Of course the rectangle of greatest area is a square.
So, if you have 60 cm, each side must be 15 cm
and the largest area is 225 cm^2
So, if you have 60 cm, each side must be 15 cm
and the largest area is 225 cm^2
Answered by
R_scott
the rectangle that encloses the maximum area is a square
2 L + 2 W = 60 ... L + W = 30 ... L = 30 - W
A = L * W ... substituting ... A = W (30 - W) = 30 W - W^2
max area is on the axis of symmetry of the parabola
... W = -b / 2 a = -30 / (2 * -1) = 15
substitute back to find L ... (see the square)
2 L + 2 W = 60 ... L + W = 30 ... L = 30 - W
A = L * W ... substituting ... A = W (30 - W) = 30 W - W^2
max area is on the axis of symmetry of the parabola
... W = -b / 2 a = -30 / (2 * -1) = 15
substitute back to find L ... (see the square)
Answered by
R_scott
if you're supposed to use calculus
A = 30 W - W^2 ... differentiating ... dA/dW = 30 - 2 W
the slope of the tangent line (1st derivative) is zero at the maximum A
dA/dW = 30 - 2W = 0 ... 30 = 2 W ... W = 15
A = 30 W - W^2 ... differentiating ... dA/dW = 30 - 2 W
the slope of the tangent line (1st derivative) is zero at the maximum A
dA/dW = 30 - 2W = 0 ... 30 = 2 W ... W = 15