The perimeter of a rectangular garden is 35 feet. The length of the garden is 1 foot more than 2 times its width.
Write an equation to represent the perimeter of the garden in terms of its width (w).
What are the length and width of the garden in feet?
2(2w+1) + 2 W = 35
4 w + 2 + 2 w = 35
6 w = 33
w = 5.5
then L = 2 w + 1 = 12
To write an equation that represents the perimeter of the garden in terms of its width, we need to understand the relationship between the length, width, and perimeter.
Let's assume the width of the garden is 'w' feet. According to the problem, the length of the garden is "1 foot more than 2 times its width." In mathematical terms, the length can be represented as (2w + 1) feet.
Now, let's calculate the perimeter of the rectangular garden. Perimeter is the sum of all the sides of a shape.
Perimeter = Length + Width + Length + Width
= (2w + 1) + w + (2w + 1) + w
Simplifying the equation, we get:
Perimeter = 6w + 2
Since the problem states that the perimeter of the garden is 35 feet, we can write the equation as:
6w + 2 = 35
Now, to find the length and width of the garden in feet, we can solve this equation.
Solving the equation:
6w + 2 = 35
Subtracting 2 from both sides:
6w = 33
Dividing both sides by 6:
w = 5.5
So, the width of the garden is 5.5 feet. To find the length, we can substitute the value of the width back into the equation for the length:
Length = 2w + 1
= 2(5.5) + 1
= 11 + 1
= 12
Therefore, the length of the garden is 12 feet. Hence, the width of the garden is 5.5 feet, and the length is 12 feet.