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 original width of the garden is "x" feet.
According to the given information, the garden is two feet longer than it is wide, so the length of the garden is "x + 2" feet.
When the width is doubled, the new width becomes "2x" feet.
It is stated that fifty extra feet of fencing will be needed to keep out the rabbits when the width is doubled. This means that the perimeter of the double-width garden is fifty feet more than the perimeter of the original garden.
Perimeter of the original garden: 2(length + width)
Perimeter of the double-width garden: 2(length + (2x))
According to the given information, the perimeter of the double-width garden is fifty feet more than the perimeter of the original garden. So we can set up the equation:
2(length + (2x)) = 2(length + width) + 50
Now we can substitute the values:
2((x + 2) + 2x) = 2((x + 2) + x) + 50
Simplifying the equation:
2(3x + 2) = 2(2x + 2) + 50
6x + 4 = 4x + 4 + 50
6x - 4x = 54
2x = 54
x = 54/2
x = 27
So the original width of the garden is 27 feet.
To find the length, we can substitute this value back into the equation:
Length = Width + 2 = 27 + 2 = 29
So the original length of the garden is 29 feet.
Therefore, the dimensions of the original garden are 27 feet (width) and 29 feet (length).