Let's break this problem down step by step:

Step 1: Understanding the rectangle's properties

• We know that the length (L) of the rectangle is twice the width (W). So we can express this as: $L = 2W$
• We are also given that the area of the rectangle is 92 square units. The formula for the area of a rectangle is: $\text{Area} = L \times W$ Substituting $L = 2W$ into the area formula: $92 = (2W) \times W = 2W^2$

Step 2: Solving for the width (W)

• Rearranging the equation: $2W^2 = 92$ $W^2 = \frac{92}{2} = 46$
• Now, solve for $W$: $W = \sqrt{46} \approx 6.78 \, \text{units}$

Step 3: Finding the length (L)

• Since the length is twice the width: $L = 2W = 2 \times 6.78 \approx 13.56 \, \text{units}$

Step 4: Estimating the side length of each square

• The rectangle can be divided into two squares with equal areas. The area of each square would be half the area of the rectangle: $\text{Area of each square} = \frac{92}{2} = 46 \, \text{square units}$ Since the area of a square is given by $s^2$ (where $s$ is the side length), we have: $s^2 = 46$ Solving for $s$: $s = \sqrt{46} \approx 6.78 \, \text{units}$

Final Answer:

• The side length of each square is approximately $6.78$ units.
• The width of the rectangle is $6.78$ units.
• The length of the rectangle is $13.56$ units.

Would you like more details on any part of the solution?

5 Related Questions:

1. What is the perimeter of this rectangle?
2. How would the dimensions change if the area of the rectangle were doubled?
3. What is the diagonal length of this rectangle?
4. If the length were increased by 50%, what would the new area be?
5. Can a different rectangle have the same area but different dimensions?

Tip:

Always verify your results by recalculating the area or perimeter to ensure the solution is consistent with the problem's conditions.