Question

The perimeter of the rectangle is 24 feet. Write an equation for the perimeter of the rectangle.

Answer 1

Part 1.

Explanation

The perimeter is the sum of the measures of all sides of a geometric figure. Then, we can write the following equation.

$\begin{gathered} \text{ Perimeter }=l+w+l+w \\ \text{ Where} \\ l\text{ is the length} \\ w\text{ is the width of the rectangle} \end{gathered}$

Now, we replace the know values into the equation.

$\begin{gathered} \text{ Perimeter }=24ft \\ l=8ft \\ \text{ Perimeter }=l+w+l+w \\ 24ft=8ft+w+8ft+w \\ \text{ Add similar terms on the right side} \\ 24ft=16ft+2w \end{gathered}$

Answer

An equation for the perimeter of the rectangle is:

$24ft=16ft+2w$Part 2.

Explanation.

We solve for w the above equation.

$\begin{gathered} 24ft=16ft+2w \\ \text{ Subtract }16ft\text{ from both sides} \\ 24ft-16ft=16ft+2w-16ft \\ 8ft=2w \\ \text{ Divide by 2 from both sides} \\ \frac{8ft}{2}=\frac{2w}{2} \\ 4ft=w \end{gathered}$

Answer

The width of the rectangle is 4 feet.