a person has a rectangular garden one length of the garden lies along the patio wall. however the rest of the garden is enclosed by 30 ft of fencing. if the length of the garden is three times its width, what is the area of the garden
To find the area of the garden, we first need to determine the dimensions of the garden. Let's assume that the width of the garden is "x" feet.
Since the length of the garden is three times its width, the length can be expressed as 3x feet.
Now, let's consider the fencing. We know that the length of the garden lies along the patio wall, which means this side does not require fencing. Hence, the other three sides of the garden require fencing.
The total fencing required is given as 30 feet. We can calculate the fencing required for all three sides by subtracting the length from the total fencing.
Total fencing required = fencing for width + fencing for length + fencing for width, which is equal to
30 = x + 3x + x
Simplifying the equation, we get:
30 = 5x
Now, let's solve for x by rearranging the equation:
5x = 30
x = 30/5
x = 6
So, the width of the garden is 6 feet. Since the length is three times the width, the length is 3 * 6 = 18 feet.
Finally, to find the area of the garden, we multiply the length by the width:
Area = Length * Width = 18 ft * 6 ft = 108 square feet.
Therefore, the area of the garden is 108 square feet.
Let's break down the problem step-by-step:
Step 1: Define the variables:
Let's say the width of the garden is 'w'.
Since the length of the garden is three times its width, the length would be '3w'.
Step 2: Calculate the perimeter of the garden:
The garden has two equal widths and two equal lengths.
So, the perimeter of the garden can be calculated as:
Perimeter = 2 * (Length + Width)
Perimeter = 2 * (3w + w)
Perimeter = 2 * (4w)
Perimeter = 8w
Step 3: Use the information about the fence:
According to the problem, the remaining part of the garden is enclosed by 30 ft of fencing.
Since the length of the garden lies along the patio wall, the length of the fenced part would be '3w'.
Therefore, we can set up an equation using the perimeter:
8w - 3w = 30
5w = 30
w = 30/5
w = 6
Step 4: Calculate the area of the garden:
Now that we know the width of the garden is 6 ft, we can calculate the length:
Length = 3w
Length = 3 * 6
Length = 18 ft
The area of a rectangle is given by:
Area = Length * Width
Area = 18 * 6
Area = 108 square feet
So, the area of the garden is 108 square feet.
L = 3W
L + 2W = 30
Substitute 3W for L in the second equation and solve for W. Insert that value into the first equation to solve for L. Check by putting both values into the second equation.
Area = L * W