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




May 19, 19 09:20 AM
Basic math review game  The one and only math adventure game online. Embark on a quest to solve math problems!
Basic math formulas
Algebra word problems
New math lessons
Your email is safe with us. We will only use it to inform you about new math lessons.
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
May 19, 19 09:20 AM
Basic math review game  The one and only math adventure game online. Embark on a quest to solve math problems!