Suppose the length of the triangle is x, if the perimeter of the rectangle is 100 ft, the width of the rectangle will be (50-x) ft. Area of rectangle will be: A=length*width A=x(50-x) A=50x-x^2 at maximum area, dA/dx=0 thus dA/dx=50-2x=0 solving for x we get 2x=50 x=25 thus for maximum area length=25 ft the size of the width will be 50-x=50-25=25 ft thus the maximum area will be: 25*25=625 sq. feet
