Betty bought 105 ft of fencing to enclose a vegetable garden in her backyard. The garden is to be a rectangle, twice as long as it is wide, with a fence across the middle parallel to the width. What should be the dimension of the garden in feet?
3W + 2L = 3W + 4W = 105
W = 105/7 = 15 ft
L = 30 ft
To find the dimensions of the garden, let's assume the width of the garden to be 'w' feet. Since the garden is twice as long as it is wide, the length can be expressed as '2w' feet.
Now, we can calculate the amount of fencing required for the entire perimeter of the garden. The perimeter of a rectangle is given by the formula: P = 2(l + w), where P represents the perimeter, l represents the length, and w represents the width.
In this scenario, the perimeter is given as 105 feet. We can set up the equation as follows:
105 = 2(2w + w)
Simplifying this equation gives:
105 = 6w
Now we can solve for 'w' by dividing both sides of the equation by 6:
w = 105 / 6
w = 17.5
Since the width cannot be a decimal, we need to round it to the nearest whole number. Therefore, the width of the garden is approximately 18 feet.
Finally, we can find the length of the garden by multiplying the width by 2:
Length = 2w = 2(18) = 36 feet.
So, the dimensions of the garden should be approximately 18 feet wide and 36 feet long.