Question

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?

Answer 1

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