Sure, let's solve this step by step.
1. Understand the Given Information:
- The perimeter of the room is given as 24 cm.
- The length of the room is given as 8 cm.
2. Perimeter Formula:
- The formula for the perimeter [tex]\( P \)[/tex] of a rectangle is:
[tex]\[
P = 2 \times (\text{length} + \text{width})
\][/tex]
3. Substitute the Known Values:
- Substituting the known values into the perimeter formula, we get:
[tex]\[
24 = 2 \times (8 + \text{width})
\][/tex]
4. Solve for Width:
- First, divide both sides of the equation by 2:
[tex]\[
12 = 8 + \text{width}
\][/tex]
- Then, subtract the length from both sides to isolate the width:
[tex]\[
\text{width} = 12 - 8
\][/tex]
- So, the width of the room is:
[tex]\[
\text{width} = 4 \, \text{cm}
\][/tex]
5. Calculate the Area:
- The formula for the area [tex]\( A \)[/tex] of a rectangle is:
[tex]\[
A = \text{length} \times \text{width}
\][/tex]
- Substituting the known length and the calculated width, we get:
[tex]\[
A = 8 \times 4
\][/tex]
- Therefore, the area of the room is:
[tex]\[
A = 32 \, \text{cm}^2
\][/tex]
So, the width of the room is 4 cm and the area of the room is 32 cm².
