Question

what should be the slope of a rectangular field of a given area, if it is to be enclosed by the least of fencing? plz answer it!!!

Answer 1

Do you mean shape?

Answer 2

yeah.. it is a field.. rectangle..

Answer 3

Suppose the length of the fence is F, and the length of the field is x, so the width of the field is (F-2x)/2. Area of the field is\[A(x)=x(F-2x)/2=-x^2+Fx/2\]

Answer 4

Note that the area function is a quadratic with a negative leading coefficient. That means that the maximum value of the function will occur at the vertex. To find the x value of the vertex, we use x=-b/2a, so\[x=(-F/2)/-2=F/4\]This makes each length one fourth of the perimeter, so the width is, also. That makes the field a square.