Answer :
To solve the problem, let's break it down step by step:
1. Understand the problem:
- You have a rectangular room with an area of 156 square feet.
- One side of the rectangle (length) is 13 feet.
- You need to find the perimeter of the room.
2. Identify the formulas needed:
- The area of a rectangle is given by the formula:
[tex]\[ \text{Area} = \text{length} \times \text{width} \][/tex]
- The perimeter of a rectangle is given by the formula:
[tex]\[ \text{Perimeter} = 2 \times (\text{length} + \text{width}) \][/tex]
3. Find the width:
- You know the area is 156 square feet and the length is 13 feet.
- Use the area formula to solve for the width:
[tex]\[
156 = 13 \times \text{width}
\][/tex]
- Solving for width, divide both sides by 13:
[tex]\[
\text{width} = \frac{156}{13} = 12 \text{ feet}
\][/tex]
4. Calculate the perimeter:
- Now that you have both the length (13 feet) and the width (12 feet), use the perimeter formula:
[tex]\[
\text{Perimeter} = 2 \times (13 + 12) = 2 \times 25 = 50 \text{ feet}
\][/tex]
5. Choose the correct system of equations:
- From the options provided, you need to choose the one that fits the situation:
- Choice A:
- [tex]\( 156 = 13 \times w \)[/tex] correctly represents the area equation.
- [tex]\( P = 2(13 + w) \)[/tex] correctly represents the perimeter equation in terms of length and width.
Therefore, based on your calculations, the correct system of equations to use is option A. The width of the room is 12 feet, and the perimeter is 50 feet.
1. Understand the problem:
- You have a rectangular room with an area of 156 square feet.
- One side of the rectangle (length) is 13 feet.
- You need to find the perimeter of the room.
2. Identify the formulas needed:
- The area of a rectangle is given by the formula:
[tex]\[ \text{Area} = \text{length} \times \text{width} \][/tex]
- The perimeter of a rectangle is given by the formula:
[tex]\[ \text{Perimeter} = 2 \times (\text{length} + \text{width}) \][/tex]
3. Find the width:
- You know the area is 156 square feet and the length is 13 feet.
- Use the area formula to solve for the width:
[tex]\[
156 = 13 \times \text{width}
\][/tex]
- Solving for width, divide both sides by 13:
[tex]\[
\text{width} = \frac{156}{13} = 12 \text{ feet}
\][/tex]
4. Calculate the perimeter:
- Now that you have both the length (13 feet) and the width (12 feet), use the perimeter formula:
[tex]\[
\text{Perimeter} = 2 \times (13 + 12) = 2 \times 25 = 50 \text{ feet}
\][/tex]
5. Choose the correct system of equations:
- From the options provided, you need to choose the one that fits the situation:
- Choice A:
- [tex]\( 156 = 13 \times w \)[/tex] correctly represents the area equation.
- [tex]\( P = 2(13 + w) \)[/tex] correctly represents the perimeter equation in terms of length and width.
Therefore, based on your calculations, the correct system of equations to use is option A. The width of the room is 12 feet, and the perimeter is 50 feet.
