Question

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

Answer 1

is this a calculus or algebra question..?

Answer 2

algebra

Answer 3

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

Answer 4

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

Answer 5

so a=27*13.5-13.5^2?

Answer 6

that's correct

Answer 7

thank you for explaining it

Answer 8

glad to help