### Home > PCT > Chapter Ch9 > Lesson 9.3.2 > Problem 9-114

9-114.

A rectangular corral is to be built using 900 ft of fencing. Three sides will need fencing. The fourth side will border a river. The goal is to make a rectangular corral that has the maximum possible area under these conditions. Homework Help ✎

Sketch the situation.

Write an equation for the area of the corral as a function of

*x*, the length of the side perpendicular to the river.Graph this function.

Which value of

*x*gives you the maximum area?What is the slope of the tangent line to the area graph at this point?

2*x* + *y* = 900*y* = 900 − 2*x*

Area = (*x*)(900 − 2*x*)

Slope of the tangent line is 0.