Fencing a rectangular garden word problem

A farmer has 260 meters of fencing and wants to enclose a rectangular area of 4200 square meters. what dimensions should he use?

Area = length × width = 4200

Perimeter = 2 × length + 2 × width = 260

We have the two equations then


length × width = 4200 (1)

2 × length + 2 × width = 260 (2)


Solve for length in (1)

length = 4200 / width


Replace length = 4200 / width in (2)


2 × (4200 / width) + 2 × width = 260

Divide the entire equation by 2

4200 / width + width = 130

Multiply the entire equation by width

4200 + width² = 130 × width


Subtract 130 × width from both sides


width² - 130 × width + 4200 = 0

(width - 60) (width -70) = 0

width = 60 or width = 70


If width = 60, then length = 70 since 60 × 70 = 4200


If width = 70, then length = 60 since 60 × 70 = 4200


Furthermore, perimeter = 2 × 60 + 2 × 70 = 120 + 140 = 260


The dimensions the farmer should the use are 60 and 70

Comments for Fencing a rectangular garden word problem

Average Rating starstarstarstarstar

Click here to add your own comments

Aug 21, 2018
Rating
starstarstarstarstar
Confused towards the end NEW
by: Anonymous

How did you subtract 130 x width in both sides at the end?

Click here to add your own comments

Join in and write your own page! It's easy to do. How? Simply click here to return to Algebra word problems.




Recent Articles

  1. Distance between a Point and a Line - Formula, proof, and Examples

    Apr 23, 19 08:22 AM

    The easy way to find the distance between a point and a line. Learn how to derive the formula the easy way

    Read More

New math lessons

Your email is safe with us. We will only use it to inform you about new math lessons.

            Follow me on Pinterest


Math quizzes

 Recommended

Scientific Notation Quiz

Graphing Slope Quiz

Adding and Subtracting Matrices Quiz  

Factoring Trinomials Quiz 

Solving Absolute Value Equations Quiz  

Order of Operations Quiz

Types of angles quiz


Tough algebra word problems

Tough Algebra Word Problems.

If you can solve these problems with no help, you must be a genius!

Recent Articles

  1. Distance between a Point and a Line - Formula, proof, and Examples

    Apr 23, 19 08:22 AM

    The easy way to find the distance between a point and a line. Learn how to derive the formula the easy way

    Read More

K-12 math tests


Everything you need to prepare for an important exam!

K-12 tests, GED math test, basic math tests, geometry tests, algebra tests. 

Real Life Math Skills

Learn about investing money, budgeting your money, paying taxes, mortgage loans, and even the math involved in playing baseball.