The perimeter of a small rectangular garden is 18 feet. if the length is twice the width, find the width and the length of the garden.
P = 2L + 2W
18 = 2(2W) + 2W
18 = 6W
3 = W
Why did the garden go on a diet? It wanted to be more "perimeter"! Now, let's solve this puzzle:
Let's assume the width of the garden is "x" feet. Since the length is twice the width, we can say the length is "2x" feet.
Now, to find the perimeter, we add up all the sides of the rectangle. We know that the perimeter is 18 feet, so we can set up the equation:
Perimeter = 2(length + width)
18 = 2(2x + x)
Let's simplify and solve:
18 = 2(3x)
Divide both sides by 2:
9 = 3x
Divide both sides by 3:
x = 3
So, the width of the garden is 3 feet.
Since the length is twice the width, the length is 2 times 3:
Length = 2 * 3 = 6 feet.
Thus, the width is 3 feet and the length is 6 feet.
Let's assume the width of the rectangular garden is w feet.
According to the problem, the length is twice the width, so the length can be expressed as 2w feet.
The perimeter of a rectangle can be calculated using the formula P = 2(length + width).
Since the perimeter is given as 18 feet, we can write the equation as 18 = 2(2w + w).
Simplifying the equation, we have 18 = 2(3w).
Distributing 2 on the right side of the equation, we get 18 = 6w.
Dividing both sides of the equation by 6, we have w = 3.
Therefore, the width of the garden is 3 feet.
Since the length is twice the width, the length would be 2w = 2(3) = 6 feet.
So, the width of the garden is 3 feet and the length is 6 feet.
To find the width and length of the garden, we can set up a system of equations based on the given information.
Let's assume the width of the garden is "w" feet.
According to the given information, the length of the garden is twice the width. Therefore, the length would be "2w" feet.
The formula for calculating the perimeter of a rectangle is P = 2(l + w), where P represents the perimeter, l represents the length, and w represents the width.
Given that the perimeter of the garden is 18 feet, we can substitute the values into the formula:
18 = 2(2w + w)
Simplifying the equation, we get:
18 = 2(3w)
Divide both sides of the equation by 2:
9 = 3w
Now, we can solve for "w" by dividing both sides of the equation by 3:
w = 3
Therefore, the width of the garden is 3 feet.
Substituting this value back into the length equation, we can find the length:
Length = 2w = 2(3) = 6
Hence, the width of the garden is 3 feet, and the length is 6 feet.