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A farmer has 300 feet of fencing to make a rectangular coral. What length and width will give the maximum area? What is the maximum area? 

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Trish H. | Certified Math Teacher- Individualized Instruction and Test PrepCertified Math Teacher- Individualized I...
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Draw and label a rectangle. Label the width (w) and the length (150-w). Because the coral is a rectangle and the entire field uses 300ft, one half of it (a length and width) will be 150ft, so the width is w and the length is 150-w.
 
Area is length times width which gives you (w)(150-w), when multiplied out gives 150w-w2
 
Rewrite this as -w+ 150w. Using the formula to find the x value of the vertex  -b/2a
 
we get  -150/2(-1)  which equals 75 which is the width. Therefore the width is 75ft and the length is 150-75 or 75ft. This results in a square (which is a type of rectangle) coral.