Question
A rectangular garden has a perimeter of 56 ft. The length of the garden is one more than twice the width. What are the dimensions of the garden?
Answers
GPT 3.5
Let's say the width of the garden is x feet.
So, the length of the garden is (2x + 1) feet.
The perimeter of a rectangle is given by the formula: P = 2(length + width).
Substituting the given values, we have: 56 = 2((2x + 1) + x).
Simplifying the equation, we get: 56 = 2(3x + 1).
Expanding the product on the right side, we have: 56 = 6x + 2.
Subtracting 2 from both sides of the equation, we get: 54 = 6x.
Dividing both sides of the equation by 6, we get: x = 9.
So, the width of the garden is 9 feet, and the length is (2 * 9 + 1) = 19 feet. Answer: \boxed{9 \text{ feet}, 19 \text{ feet}}.
So, the length of the garden is (2x + 1) feet.
The perimeter of a rectangle is given by the formula: P = 2(length + width).
Substituting the given values, we have: 56 = 2((2x + 1) + x).
Simplifying the equation, we get: 56 = 2(3x + 1).
Expanding the product on the right side, we have: 56 = 6x + 2.
Subtracting 2 from both sides of the equation, we get: 54 = 6x.
Dividing both sides of the equation by 6, we get: x = 9.
So, the width of the garden is 9 feet, and the length is (2 * 9 + 1) = 19 feet. Answer: \boxed{9 \text{ feet}, 19 \text{ feet}}.