A rectangular garden is two feet
longer than it is wide. If the width is
doubled, fifty extra feet of fencing will be
needed to keep out the rabbits. What are the
dimensions of the original garden
To find the dimensions of the original garden, we can follow these steps:
Let's assume the width of the original garden is x feet.
According to the given information, the length of the garden is two feet longer than its width. So, the length would be (x + 2) feet.
Now, let's consider the new width of the garden when it is doubled. It would be 2x feet.
The perimeter of a rectangle is 2 times the sum of its length and width. Thus, the original perimeter is given by:
Perimeter = 2 * (x + 2 + x) = 2 * (2x + 2) = 4x + 4
Similarly, the new perimeter is given by:
Perimeter + 50 = 2 * (2x + x) + 50 = 2 * (3x) + 50 = 6x + 50
Since we are told that 50 extra feet of fencing will be needed when the width is doubled, we can set up an equation:
Original Perimeter + 50 = New Perimeter
Therefore, we have:
4x + 4 + 50 = 6x + 50
We can now solve this equation to find the value of x:
4x + 54 = 6x + 50
54 - 50 = 6x - 4x
4 = 2x
x = 2
Hence, the original width of the garden is 2 feet, and the original length is (2 + 2) = 4 feet. Therefore, the dimensions of the original garden are 2 feet by 4 feet.