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-w2
Rewrite this as -w2 + 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.