The length of a rectangular garden is 14 feet longer than its width. if the garden's perimeter is 200 feet, what is the area of the garden in square feet?

Write an equation system based on the problem
The length of a rectangular garden is 14 feet longer than its width
∴ l = w + 14 (first equation)
The perimeter is 200 feet
∴ 2l + 2w = 200 (second equation)

Solve the equation system to find the dimension of the rectangular
Use substitution method, substitute in (w + 14) as l in the second equation
2l + 2w = 200
2(w + 14) + 2w = 200
2w + 28 + 2w = 200
4w + 28 = 200
4w = 200 - 28
4w = 172
  w = 172/4
  w = 43
The width of the rectangle is 43 feet

Find the length
l = w + 14
l = 43 + 14
l = 57
The length of the rectangle is 57 feet

Calculate the area of the rectangle
area = l × w
area = 57 × 43
area = 2,451
The area of the rectangle is 2,451 square feet.