A gardener wants to use 62 feet of fencing to enclose a rectangular shaped garden. If its length is 4 feet longer than twice its width, find the width of the garden
I'm going to have you do this question but I'll get you started. What do we already know?
Total amount of fencing = 62 feet
Width = unknown so let's refer to it by the variable W
Length = 2W + 4 (they told us in the question that the length is 2 times the width plus 4 feet)
Now let's once again use out perimeter equation and plug in what we know:
P = L + W + L + w
62 = (2W+4)+W+(2W+4)+w
Now I'm going to have you solve from this point forward because I think you'll be able to do so.
Let's suppose the width of the garden is 'w' feet.
According to the problem, the length of the garden is 4 feet longer than twice its width. So, the length can be expressed as (2w + 4) feet.
The perimeter of a rectangle is given by the formula:
Perimeter = 2(length + width)
In this case, the perimeter is equal to the given length of fencing, which is 62 feet.
So, we can write the equation as:
62 = 2((2w + 4) + w)
Now, let's solve this equation to find the value of 'w'.
62 = 2(2w + 4 + w)
62 = 2(3w + 4)
62 = 6w + 8
6w = 62 - 8
6w = 54
w = 54/6
w = 9
Therefore, the width of the garden is 9 feet.
To find the width of the garden, we need to set up an equation based on the information given.
Let's assume the width of the garden is x feet.
According to the given information, the length of the garden is 4 feet longer than twice its width. Therefore, the length would be 2x + 4 feet.
Now, we know that the perimeter of a rectangle is calculated by adding all the four sides. In this case, the perimeter is given as 62 feet.
Perimeter = 2 * (Length + Width)
Substituting the length and width from the information we have:
62 = 2 * (2x + 4 + x)
Simplifying the equation:
62 = 2 * (3x + 4)
Dividing both sides by 2:
31 = 3x + 4
Subtracting 4 from both sides:
31 - 4 = 3x
27 = 3x
Dividing both sides by 3:
27 / 3 = x
9 = x
Therefore, the width of the garden is 9 feet.