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?

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-w

^{2}Rewrite this as -w

^{2 }+ 150w. Using the formula to find the x value of the vertex -b/2awe 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.