Farmer Brown has 300 yards of fencing with which to build a rectangular corral. He wants to divide it evenly into three pens, so he adds in two divider fences.

Question

a) Write the area of the corral as function of x, so A(x)=?

 

b) Determine the maximum area enclosed by the corral. (Decimal approximations are marked incorrect.) So the maximum area equals how many square yards?

 

I can't insert a picture, but it basically looks like this: 

 

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I got the answer of A(x)=-2x^2+150x for a) and 2812.5 yd^2 for b). I started the equation with 4x+2y=300, but when I showed my teacher, she circled the "4x+2y=300" and said it was wrong. She didn't too much go into details about why it was wrong tho. Any help is greatly appreciated!

Answer 1

For a rectangle, the maximum area for a given perimeter will always be the square. So the equations are A(x) = x² and 6x = 300, which means the sides are 50 yards and the area is 2500 yards.