Final answer:
To find the length and width of a rectangular garden, you can set up a system of equations. The width can be represented as 'w' and the length is twice the width, or '2w'. The perimeter of the garden can be expressed as 2w + 2(2w) = 96 feet. Solving this equation yields a width of 16 feet and a length of 32 feet.
Step-by-step explanation:
To write a system of equations to find the length and width of a rectangular garden, we need to set up two equations based on the given information. Let's assume the width of the garden is 'w' feet. The length of the garden is twice the width, so the length would be '2w' feet.
The perimeter of a rectangle is found by adding up all the side lengths. In this case, the perimeter is given as 96 feet, so we can set up the equation: 2w + 2(2w) = 96. Simplifying this equation, we get: 6w = 96. Dividing both sides by 6, we find that w = 16. Therefore, the width of the garden is 16 feet and the length is 2w, or 32 feet.