91. Maximizing an Enclosed Area A farmer with 2000 meters of fencing wants to enclose a rectangular plot that borders a river. If the farmer does not fence the side along the river, what is the largest area that can be enclosed? What are the dimensions of the enclosed area? See the figure. 2000 - 2x

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,...
icon
Related questions
icon
Concept explainers
Topic Video
Question

help

**Maximizing an Enclosed Area**

A farmer with 2000 meters of fencing wants to enclose a rectangular plot that borders a river. If the farmer does not fence the side along the river, what is the largest area that can be enclosed? What are the dimensions of the enclosed area? See the figure.

**Explanation of the Diagram:**

The diagram illustrates a rectangular plot of land adjacent to a river, with three fenced sides. The side along the river is unfenced. The two shorter sides of the rectangle are labeled as \( x \), and the longer fenced side is labeled as \( 2000 - 2x \). The river runs parallel to the longer side of the rectangle. The goal is to determine the dimensions that maximize the area of this unfenced plot.
Transcribed Image Text:**Maximizing an Enclosed Area** A farmer with 2000 meters of fencing wants to enclose a rectangular plot that borders a river. If the farmer does not fence the side along the river, what is the largest area that can be enclosed? What are the dimensions of the enclosed area? See the figure. **Explanation of the Diagram:** The diagram illustrates a rectangular plot of land adjacent to a river, with three fenced sides. The side along the river is unfenced. The two shorter sides of the rectangle are labeled as \( x \), and the longer fenced side is labeled as \( 2000 - 2x \). The river runs parallel to the longer side of the rectangle. The goal is to determine the dimensions that maximize the area of this unfenced plot.
Expert Solution
trending now

Trending now

This is a popular solution!

steps

Step by step

Solved in 2 steps with 2 images

Blurred answer
Knowledge Booster
Application of Algebra
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, algebra and related others by exploring similar questions and additional content below.
Recommended textbooks for you
Algebra and Trigonometry (6th Edition)
Algebra and Trigonometry (6th Edition)
Algebra
ISBN:
9780134463216
Author:
Robert F. Blitzer
Publisher:
PEARSON
Contemporary Abstract Algebra
Contemporary Abstract Algebra
Algebra
ISBN:
9781305657960
Author:
Joseph Gallian
Publisher:
Cengage Learning
Linear Algebra: A Modern Introduction
Linear Algebra: A Modern Introduction
Algebra
ISBN:
9781285463247
Author:
David Poole
Publisher:
Cengage Learning
Algebra And Trigonometry (11th Edition)
Algebra And Trigonometry (11th Edition)
Algebra
ISBN:
9780135163078
Author:
Michael Sullivan
Publisher:
PEARSON
Introduction to Linear Algebra, Fifth Edition
Introduction to Linear Algebra, Fifth Edition
Algebra
ISBN:
9780980232776
Author:
Gilbert Strang
Publisher:
Wellesley-Cambridge Press
College Algebra (Collegiate Math)
College Algebra (Collegiate Math)
Algebra
ISBN:
9780077836344
Author:
Julie Miller, Donna Gerken
Publisher:
McGraw-Hill Education