You have 600 offence and want to build a rectangle Area may

You have 600\' offence and want to build a rectangle Area may area. You already a wall of 200\' and a wall of 400\'

Solution

Fence = 600\'

Wall of 200\' and 400\' also can be used along with fence to construct the rectangle.

Let the rectangle have dimensions as x and y

Then area = xy

Perimeter of the rectangle = 2l +2w

= 2x+2y = Dimensions of wall + dimension of fence

2x+2y = 600+600 = 1200

x+y = 600

Eliminate one variable and get area in terms of one variable say x

y = 600-x

Area = A(x) = xy = x(600-x)

A(x) = 600x-x²

Use derivative test to get max volume

A\'(x) = 600-2x

A\"(x) = -2<0

Since second derivative is negative, setting A\' to 0 give maximum value

600-2x =0 gives x =300 is maximum

Hence the area will be maximum with length = 300 and width = 300

so that total fence = 1200\'