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?

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