## Answer :

**Answer:the length of the rectangle is 14 feet, and the width is 7 feet.**

**Step-by-step explanation:**

Let's denote the width of the rectangle as \( w \) feet. Since the length is twice the width, we can express the length as \( 2w \) feet.

The perimeter \( P \) of a rectangle is given by the formula:

\[ P = 2 \times (\text{length} + \text{width}) \]

Given that the perimeter is 42 feet, we can write the equation:

42 = 2 times (2w + w)

Solving for (w):

42 = 2(3w)

42 = 6w

w = 42/6

w = 7 feet

**So, the width of the rectangle is 7 feet. **

Now, we can find the length:

Length = 2w = 2 times 7 = 14 feet

**Therefore, the length of the rectangle is 14 feet, and the width is 7 feet.**

**Answer:**

Width = 7 ft

Length = 14 ft

**Step-by-step explanation:**

The **perimeter (P)** of a **rectangle **is twice the sum of its width (w) and length (l):

[tex]P = 2(w + l)[/tex]

Given that the length of the rectangle is twice its width, and the perimeter is 42 ft, **substitute l = 2w** and **P = 42** into the **perimeter equation**:

[tex]42=2(w+2w)[/tex]

**Solve for w**:

[tex]42=2(3w)\\\\\\6w=42\\\\\\\dfrac{6w}{6}=\dfrac{42}{6}\\\\\\w=7[/tex]

Therefore, the **width **of the rectangle is **7ft**.

To find its length, **substitute w = 7** into the expression for length:

[tex]l = 2w\\\\l=2(7)\\\\l=14[/tex]

Therefore, the **length **of the rectangle is **14 ft**.