The legnth of a rectangular floor is 2 feet more than it's 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 legnth of the rug be?
Your first job should be to determine the dimensions of the floor.
Let X = width, then
X + 2 = length.
The area is 168; therefore,
X(X+2) = 168 which expands to
X^2 + 2X - 168.
Solve that for X and X+2 then look to see how much smaller the rug should be. Post your work if you get stuck.
the rug should 2
To find the length of the rug, we need to find the dimensions of the rectangular floor first.
Let's assume the width of the floor is "x" feet.
According to the given information, the length of the floor is 2 feet more than its width. So, the length would be "x + 2" feet.
The area of the floor is given as 168 square feet. The formula for the area of a rectangle is length multiplied by width. So, we can set up the equation:
x(x + 2) = 168
Expanding the equation, we get:
x^2 + 2x = 168
Rearranging the equation and setting it to zero, we get:
x^2 + 2x - 168 = 0
Now, we can factor or use the quadratic formula to solve for "x". For this equation, let's use factoring.
We need to find two numbers whose sum is 2 and whose product is -168.
The numbers are 12 and -14.
(x + 14)(x - 12) = 0
Setting each factor to zero, we get:
x + 14 = 0 or x - 12 = 0
Solving for "x", we get:
x = -14 or x = 12
Since the width cannot be negative, we discard the solution x = -14.
Therefore, the width of the floor is 12 feet.
Now, we can find the length of the floor.
Length = x + 2
Length = 12 + 2
Length = 14 feet
Since Kim wants to leave a 2-foot border of the floor visible on all sides, we subtract 2 feet from both the width and length to find the dimensions of the rug.
Width of the rug = 12 - 2 = 10 feet
Length of the rug = 14 - 2 = 12 feet
Therefore, the length of the rug should be 12 feet.