# 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

New math lessons

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

## Recent Articles

1. ### Number Game

Dec 01, 16 06:27 AM

1. Think of any positive whole number. No fractions, no decimals,no percents. 2. Double that number. 3. Add 10 to that result in step 2. 4. Divide