Let's solve the problem step by step.

Step 1: Define the variables.

• Let the length of the rectangular floor be $L$ meters.
• The width of the rectangular floor is 1 meter less than its length, so the width is $W = L - 1$ meters.

Step 2: Use the formula for the area of a rectangle.

The area $A$ of a rectangle is given by: $A = L \times W$ Substitute the given area and the expression for the width: $6 = L \times (L - 1)$

Step 3: Solve the quadratic equation.

Expand and rearrange the equation: $L^2 - L - 6 = 0$ Now, factor the quadratic equation: $(L - 3)(L + 2) = 0$

Step 4: Find the values of $L$.

Set each factor equal to zero: $L - 3 = 0 \quad \text{or} \quad L + 2 = 0$ $L = 3 \quad \text{or} \quad L = -2$ Since a length can't be negative, we discard $L = -2$ and accept $L = 3$.

Step 5: Find the width.

If $L = 3$ meters, then the width $W$ is: $W = L - 1 = 3 - 1 = 2 \text{ meters}$

Final Answer:

The dimensions of the rectangular floor are:

• Length: 3 meters
• Width: 2 meters

Would you like any more details or explanations? Here are 5 questions that expand on this problem:

1. How would the solution change if the area were 12 square meters?
2. What if the width were 2 meters more than the length? How would you solve it?
3. Can you generalize a formula for the dimensions given any area and a similar width-length relationship?
4. How would the problem change if the width was exactly half of the length?
5. How can you verify that the solution to the quadratic equation is correct?

Tip: When solving quadratic equations, always check both solutions to ensure they make sense in the context of the problem.