## stevetron one year ago Suppose you have 54 feet of fencing to enclose a rectangular dog pen. The function A=27x-x^2, where x = width, gives you the area of the dog pen in square feet. What width gives you the maximum area? What is the maximum area? Round to the nearest tenth as necessary. a.width = 13.5 ft; area = 546.8 ft2 b.width = 27 ft; area = 182.3 ft2 c.width = 13.5 ft; area = 182.3 ft2 d.width = 27 ft; area = 391.5 ft2

1. campbell_st

is this a calculus or algebra question..?

2. stevetron

algebra

3. campbell_st

ok... find the line of symmetry, use $x = \frac{-b}{2 \times a}$ so in your question b = 27 and a = -1 substitute them to find the width for the max area

4. campbell_st

what you have found is the line of symmetry for the parabola. The maximum area lies on the line of symmetry so given a quadratic $ax^2 + bx + c$ the line of symmetry is $x = \frac{-b}{2a}$ then to find the max area, substitute the value into the original equation

5. stevetron

so a=27*13.5-13.5^2?

6. campbell_st

that's correct

7. stevetron

thank you for explaining it

8. campbell_st