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