David has available 400 yards of fencing and wishes to enclose a rectangular area.?

Express the area A of the rectangle as a function of the width x of the rectangle.





The answer is -x^2+200x. How do you get the answer?|||Allow x to be the width. You have 400 yards total, and are is length x width. So what is the length?





The length is (400 - 2x) / 2 , that is, the length of one side is 400 yards minus the two widths of x, and divided by 2 because there are two lengths. So if:





length = (400 - 2x) / 2


width = x


area = length x width





then.....





area = (x)((400 - 2x) / 2)





divide out the 2 and you get area = (x)(200 - x)





now multiply the x through and you get.........





area = 200x - x^2|||Width is x, and 2 * (length+width) = 400


So length = 400/2 - width = 200-x


So area = length * width = (200-x) * x = -x^2 + 200x.


.|||Area of a rectangle is length (L) x width (W).


And are given width=X


And are given 2X+2L=400 yds


So you derive L=(400-2X)/2


Plugging that into the A=L x W formula gives you:


A = (400-2X)/2 x X


That renders down to:


A = (200-X) x X


A = 200X-X^2