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?

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12-02-2018
Mathematics

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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?

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gustanika gustanika · Answer 1 · 2018-02-12T08:28:25+01:00

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.