Nya is building a garden in her yard. She has 24 feet of fencing for her garden and wants it to be in the shape of a rectangle with a length of 3 feet. What does the width need to be for this to work?
Let's call the width of the rectangle x. The perimeter of a rectangle is given by the formula: P = 2l + 2w, where P is the perimeter, l is the length, and w is the width. In this case, the perimeter is 24 feet and the length is 3 feet. Therefore, we can write the equation 24 = 2(3) + 2x. Simplifying this equation gives 24 = 6 + 2x. Subtracting 6 from both sides gives 18 = 2x. Finally, dividing both sides by 2 gives x = 9 feet. Therefore, the width needs to be 9 feet for the garden to work.
To find the width of the garden, we can use the formula for the perimeter of a rectangle:
Perimeter = 2 * (Length + Width)
Given that the length is 3 feet and the total fencing available is 24 feet, we can substitute these values into the formula:
24 = 2 * (3 + Width)
Simplifying the equation:
24 = 6 + 2 * Width
Subtracting 6 from both sides:
18 = 2 * Width
Dividing both sides by 2:
Width = 9 feet
Therefore, the width of the garden needs to be 9 feet for it to work with a length of 3 feet.
To determine the width of the garden, we can use the given information about the total length of the fencing.
Let's break down the problem step by step:
1. The perimeter of a rectangle is calculated by adding all of its sides. In this case, the perimeter is equal to 24 feet.
2. Since the length of the rectangle is given as 3 feet, we have one side with a known measurement. Let's call the width of the rectangle "w".
3. The perimeter formula for a rectangle is: Perimeter = 2 × (Length + Width)
4. Substituting in the given values, we get: 24 = 2 × (3 + w)
5. Simplifying the equation: 24 = 6 + 2w
6. We isolate the variable "w" by subtracting 6 from both sides: 24 - 6 = 2w
7. Simplifying further: 18 = 2w
8. To solve for "w", we divide both sides of the equation by 2: 18 ÷ 2 = w
9. Thus, the width of the garden needs to be 9 feet for the perimeter to be 24 feet.
Therefore, the width of the garden should be 9 feet for Nya's garden to have a length of 3 feet and a total fence length of 24 feet.