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
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