



 
Hi Kate. You know the area and you know you need to fence three sides. Let P = the length of fence parallel to the side of the barn and let F be the total length of fencing that you need. That means the other side of the rectangle is (FP)/2 units long. The area of a rectangle is the length times the width, so this is P times (FP)/2. You know the area is 21 square meters. So: P (FP) / 2 = 21. When you multiply this out, you have a quadratic relationship. You are trying to find the minimum F. Think about parabolas which are quadratic relationships. They have a minimum point at the vertex. Can you write the equation in vertexgraphing form and find the vertex? That will give you the correct values of P and F, which you can use to determine the other dimension of the carrot patch using (FP)/2. Cheers,  


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