Short Story question

Question

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? 

Answer 1

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.