The length of a rectangular floor is 2 feet more than its width. The area of the floor is 168 square feet. Kim wants to use a rug in the middle of the room and leave a 2 foot border of the floor visible on all sides. What should the length (the shorter side) of the rug be?
Floor: w(w+2) = 168
Rug: (w-4) by (w+2-4)
To find the length of the rug, we need to first determine the dimensions of the rectangular floor.
Let's assume the width of the floor is x feet. According to the problem, the length of the floor is 2 feet more than its width, so the length would be (x + 2) feet.
The area of a rectangle can be calculated by multiplying its length by its width. In this case, the area of the floor is given as 168 square feet. So, we can create the equation:
x(x + 2) = 168
Simplifying this equation will help us find the value of x:
x^2 + 2x = 168
Rearranging the equation:
x^2 + 2x - 168 = 0
Now, we can solve this quadratic equation by factoring, completing the square, or using the quadratic formula. Let's choose factoring:
(x + 14)(x - 12) = 0
Setting each factor equal to zero, we have:
x + 14 = 0 OR x - 12 = 0
Solving each equation:
x = -14 OR x = 12
Since the width cannot be negative, we discard the negative value. Therefore, the width of the floor is 12 feet.
Now, let's find the length of the floor:
Length = Width + 2 = 12 + 2 = 14 feet
According to the problem, Kim wants to use a rug in the middle of the room and leave a 2-foot border visible on all sides. This means the length of the rug should be 2 feet less than the width and the length of the floor.
Length of the rug = Length of the floor - 2 = 14 - 2 = 12 feet
Therefore, the length (the shorter side) of the rug should be 12 feet.