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 longer side) of the rug be?
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first first the dimensions of the room ....
x(x+2) = 168
x^2 + 2x - 168 = 0
(x-12)(x+14) = 0
I am sure you can take it from here
To find the length (the longer side) of the rug, we'll need to figure out the dimensions of the rectangular floor first.
Let's call the width of the floor "x" feet. Since the length is 2 feet more than the width, we can express the length as "x + 2" feet.
The area of a rectangle is calculated by multiplying its length by its width. In this case, we know the area is 168 square feet. Using the dimensions we just defined, we can set up the following equation:
(x + 2) * x = 168
To solve this equation, we'll multiply the terms inside the parentheses:
x^2 + 2x = 168
Next, we'll subtract 168 from both sides:
x^2 + 2x - 168 = 0
Now, we can either factor the quadratic equation or use the quadratic formula to solve for x. In this case, factoring might be easier:
(x - 12)(x + 14) = 0
Setting each factor equal to zero, we have:
x - 12 = 0 or x + 14 = 0
Solving for x, we find two possible solutions:
x = 12 or x = -14
Since a length cannot be negative, we discard the x = -14 solution. Therefore, the width of the rectangular floor is 12 feet. And since the length is 2 feet more than that, the length of the rectangular floor is 12 + 2 = 14 feet.
Given that Kim wants to leave a 2-foot border on all sides of the rug, the dimensions of the rug will be 2 feet less than the dimensions of the room. So, the width of the rug will be 12 - 2 = 10 feet, and the length of the rug will be 14 - 2 = 12 feet.
Therefore, the length (the longer side) of the rug should be 12 feet.