Question

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

Answer 1

To determine the perimeter of a rectangle where it is known to be 24 feet, use the formula 2l + 2w = 24. Specified lengths and widths are not provided, making individual calculation impossible without additional information. This formula is fundamental in geometry and solving real-world measurement problems.

Step-by-step explanation:

To find the equation for the perimeter of a rectangle when it is given to be 24 feet, we must use the standard formula for the perimeter of a rectangle which is P = 2l + 2w, where P is the perimeter, l is the length, and w is the width. However, the question doesn't provide individual values for the length and width. If we had been given the length and width, we would simply plug in those values and solve for the perimeter. Since the perimeter is already provided as 24 feet, the equation based on the given perimeter is 2l + 2w = 24.

Occasionally, problems might involve scale factors or proportions, such as the example where a proportion is given: 1/48 = w/16. In this case, cross-multiply to solve for the width, w. But this is not directly related to the question about the rectangle's perimeter since no specific ratios or scale factors are given for this problem.

If we needed to apply this to a real-world problem like measuring an actual carpet or determining the space between buildings as per a scale on a map, using consistent units like feet to measure lengths would be essential. Also, converting other measurements, such as from yards to feet or inches to feet, might be necessary before calculating the perimeter.

Answer 2

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} \\ (8ft)/(2)=(2w)/(2) \\ 4ft=w \end{gathered}`

Answer

The width of the rectangle is 4 feet.