Let the width of the rectangle be $w$ cm, and the length be $2w$ cm (since the length is twice the width).

Step 1: Use the area formula for the rectangle.

The area of a rectangle is given by: $\text{Area} = \text{Length} \times \text{Width}$ Substituting the known values: $84 = 2w \times w$ $84 = 2w^2$

Step 2: Solve for $w$.

$w^2 = \frac{84}{2} = 42$ $w = \sqrt{42} \approx 6.48 \, \text{cm}$

Step 3: Find the length.

Since the length is twice the width: $\text{Length} = 2w = 2 \times 6.48 \approx 12.96 \, \text{cm}$

Step 4: Calculate the perimeter.

The perimeter of a rectangle is given by: $\text{Perimeter} = 2(\text{Length} + \text{Width})$ Substituting the values of length and width: $\text{Perimeter} = 2(12.96 + 6.48) = 2 \times 19.44 = 38.88 \, \text{cm}$

Thus, the perimeter of the rectangle is approximately 38.88 cm.

Would you like more details or have any questions?

Here are 5 related questions:

1. How do you find the width if only the perimeter and area are given?
2. What if the length was three times the width, how would the solution change?
3. How can you calculate the diagonal of the rectangle?
4. What is the relationship between area and perimeter for a square?
5. How can you express the perimeter formula in terms of area and length?

Tip: Always double-check units when working with area and perimeter to avoid mix-ups!