Questions: Write the equations for the system and then solve. The perimeter of a rectangular floor is 138 feet. Find the dimensions of the floor if the length is twice the width. What are it's dimensions?

Write the equations for the system and then solve.

Define variables

Let the width of the rectangular floor be $w$ feet. Since the length is twice the width, the length is $2w$ feet.

Write the perimeter equation

The perimeter $P$ of a rectangle is given by:
$$P = 2(\text{length} + \text{width})$$
Substitute the given perimeter and expressions for length and width:
$$138 = 2(2w + w)$$

Simplify the equation

Simplify the equation:
$$138 = 2(3w)$$
$$138 = 6w$$

Solve for $w$

Divide both sides by 6:
$$w = \frac{138}{6} = 23$$

Find the length

Since the length is twice the width:
$$\text{length} = 2w = 2(23) = 46$$

The dimensions of the floor are:
$$\boxed{\text{width} = 23 \text{ feet}, \text{length} = 46 \text{ feet}}$$

The dimensions of the floor are:
$$\boxed{\text{width} = 23 \text{ feet}, \text{length} = 46 \text{ feet}}$$