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 need to set up an equation based on the information given in the problem.
Let's represent the width of the original garden as "w" and the length as "l". According to the problem, the length is two feet longer than the width, so we can express the length as "w + 2".
The problem also states that if the width is doubled, 50 extra feet of fencing will be needed. This means that the perimeter of the modified garden (doubled width) is 50 feet greater than the perimeter of the original garden.
The perimeter of a rectangle is given by the formula: P = 2w + 2l
Let's set up an equation using this formula for both the original and modified garden:
Perimeter of original garden: 2w + 2(w + 2) = P1
Perimeter of modified garden: 2(2w) + 2(w + 2) = P1 + 50
Now, we can solve these equations to find the value of w and calculate the dimensions of the original garden.
First, let's simplify the equations:
2w + 2w + 4 = P1
4w + 4 = P1
4w + 4 = P1 + 50
Now, let's solve the equations:
4w + 4 = 4w + 50
Subtracting 4w from both sides: 4 = 50
As we can see, the equations do not yield a valid solution. This means there is no solution for the original garden dimensions that satisfies the given conditions.