You are enclosing a rectangular garden with 60 feet of ornamental fencing. the area of the garden is 200 square feet. what are the dimensions of the garden?
Accepted Solution
A:
The perimeter is equal to 60 feet and has the formula:
Perimeter = 2 l + 2 w
60 = 2 l + 2 w
The area is equal to 200 square feet and has the formula:
Area = l w
200 = l w
Rewriting area in terms of l:
l = 200 / w
Combining this with the perimeter formula:
60 = 2 (200 / w) + 2 w
60 = 400 / w + 2 w
Multiplying all by w:
60 w = 400 + 2 w^2
Dividing by 2 and rearranging:
w^2 – 30 w = - 200
Completing the square:
(w – 15)^2 = - 200 + (-15)^2
(w – 15)^2 = 25
w – 15 = ±5
w = 10, 20
Hence the dimensions of the garden is 10 feet by 20 feet