SOLUTION: 1. You have 150 yards of fencing to enclose a rectangular region. One side of the rectangle does not need fencing. Find the dimensions of the rectangle that maximize the enclosed a

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equations Lessons  -> Quadratic Equation Lesson -> SOLUTION: 1. You have 150 yards of fencing to enclose a rectangular region. One side of the rectangle does not need fencing. Find the dimensions of the rectangle that maximize the enclosed a      Log On


   

Question 744516: 1. You have 150 yards of fencing to enclose a rectangular region. One side of the rectangle does not need fencing. Find the dimensions of the rectangle that maximize the enclosed area. What is the maximum area?Complete the following steps to solve the above problem:
Write the equation for the area of the rectangular region:
A =
Write the equation for the fencing required:
150 =
Solve the equation for fencing for y.
Substitute the result of step c) into the area equation to obtain A as function of x.
Write the function in the form of f(x)=ax^2+bx+c.
Calculate –b/2a. If a < 0, the function has a maximum at this value.
This means that the area inside the fencing is maximized when x = ?
Find the length of side y.
Find the maximum area.
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