A square vegetablegarden is to be tilled and then enclosed with a fence.If the fence costs $1 per
foot and the cost of preparing the soil is $0.50per feet squared, determine the size of the garden
that can be enclosed for $120.
Solution
x is the side length of the square.
Cost of fence: (1)(4x) = 4x
Cost of preparing soil: (1/2)(x^2) = (1/2)x^2
Total cost: (1/2)x^2 + 4x
(1/2)x^2 + 4x = 120
2[(1/2)x^2 + 4x] = 2[120]
x^2 + 8x = 240
x^2 + 8x - 240 = 0
(x - 12)(x + 20) = 0
x = -20, 12
x > 0 => x = 12
The area of the garden is 144 square feet..
A square vegetablegarden is to be tilled and then enclosed with a fe.pdf
1. A square vegetablegarden is to be tilled and then enclosed with a fence.If the fence costs $1 per
foot and the cost of preparing the soil is $0.50per feet squared, determine the size of the garden
that can be enclosed for $120.
Solution
x is the side length of the square.
Cost of fence: (1)(4x) = 4x
Cost of preparing soil: (1/2)(x^2) = (1/2)x^2
Total cost: (1/2)x^2 + 4x
(1/2)x^2 + 4x = 120
2[(1/2)x^2 + 4x] = 2[120]
x^2 + 8x = 240
x^2 + 8x - 240 = 0
(x - 12)(x + 20) = 0
x = -20, 12
x > 0 => x = 12
The area of the garden is 144 square feet.
![A square vegetablegarden is to be tilled and then enclosed with a fence.If the fence costs $1 per
foot and the cost of preparing the soil is $0.50per feet squared, determine the size of the garden
that can be enclosed for $120.
Solution
x is the side length of the square.
Cost of fence: (1)(4x) = 4x
Cost of preparing soil: (1/2)(x^2) = (1/2)x^2
Total cost: (1/2)x^2 + 4x
(1/2)x^2 + 4x = 120
2[(1/2)x^2 + 4x] = 2[120]
x^2 + 8x = 240
x^2 + 8x - 240 = 0
(x - 12)(x + 20) = 0
x = -20, 12
x > 0 => x = 12
The area of the garden is 144 square feet.](https://image.slidesharecdn.com/asquarevegetablegardenistobetilledandthenenclosedwithafe-230323140644-ae84c65a/85/A-square-vegetablegarden-is-to-be-tilled-and-then-enclosed-with-a-fe-pdf-1-320.jpg)
