9. Forming a Pen We want to form a rectangular pen of area 100 square feet. One side of the pen is to be formed by an existing building and the other three sides by a fence (see Figure 2.106). Let W be the length, in feet, of the sides of the rectangle perpen- dicular to the building, and let L be the length, in feet, of the other side. W L FIGURE 2.106 a. Find a formula for the total amount of fence needed in terms of W and L. b. Express, as an equation involving W and L, the requirement that the total area formed be 100 square feet. c. Solve the equation you found in part b for L. d. Use your answers to parts a and c to find a formula for F, the total amount, in feet, of fence needed as a function of W alone

9. Forming a Pen We want to form a rectangular pen of area 100 square feet. One side of the pen is to be formed by an existing building and the other three sides by a fence (see Figure 2.106). Let W be the length, in feet, of the sides of the rectangle perpen- dicular to the building, and let L be the length, in feet, of the other side. W L FIGURE 2.106 a. Find a formula for the total amount of fence needed in terms of W and L. b. Express, as an equation involving W and L, the requirement that the total area formed be 100 square feet. c. Solve the equation you found in part b for L. d. Use your answers to parts a and c to find a formula for F, the total amount, in feet, of fence needed as a function of W alone

Algebra and Trigonometry (6th Edition)

6th Edition

ISBN:9780134463216

Author:Robert F. Blitzer

Publisher:Robert F. Blitzer

ChapterP: Prerequisites: Fundamental Concepts Of Algebra

Section: Chapter Questions

Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...

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Question

9. Forming a Pen We want to form a rectangular pen
of area 100 square feet. One side of the pen is to be
formed by an existing building and the other three
sides by a fence (see Figure 2.106). Let W be the
length, in feet, of the sides of the rectangle perpen-
dicular to the building, and let L be the length, in
feet, of the other side.
W
L
FIGURE 2.106
a. Find a formula for the total amount of fence
needed in terms of W and L.
b. Express, as an equation involving W and L, the
requirement that the total area formed be 100
square feet.
c. Solve the equation you found in part b for L.
d. Use your answers to parts a and c to find a
formula for F, the total amount, in feet, of fence
needed, as a function of W alone.
e. Make a graph of F versus W.
f. Determine the dimensions of the rectangle that
requires a minimum amount of fence.

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