Answer :
Certainly! Let's go through the steps to find the perimeter and area of the rectangle given that the length is 15 inches and the width is 5 inches.
### Finding the Perimeter:
1. Formula for Perimeter of a Rectangle:
The perimeter [tex]\( P \)[/tex] of a rectangle is calculated using the formula:
[tex]\[ P = 2 \times (\text{length} + \text{width}) \][/tex]
2. Substitute the given values:
The length [tex]\( l = 15 \)[/tex] inches, and the width [tex]\( w = 5 \)[/tex] inches. Substitute these values into the formula:
[tex]\[ P = 2 \times (15 + 5) \][/tex]
3. Perform the operations inside the parentheses first:
[tex]\[ 15 + 5 = 20 \][/tex]
4. Multiply the sum by 2:
[tex]\[ P = 2 \times 20 = 40 \][/tex]
5. Units:
Since we're dealing with inches, the perimeter will be in inches.
- Perimeter:
[tex]\[ P = 40 \text{ inches} \][/tex]
### Finding the Area:
1. Formula for Area of a Rectangle:
The area [tex]\( A \)[/tex] of a rectangle is calculated using the formula:
[tex]\[ A = \text{length} \times \text{width} \][/tex]
2. Substitute the given values:
Again, the length [tex]\( l = 15 \)[/tex] inches, and the width [tex]\( w = 5 \)[/tex] inches. Substitute these values into the formula:
[tex]\[ A = 15 \times 5 \][/tex]
3. Multiply the length by the width:
[tex]\[ 15 \times 5 = 75 \][/tex]
4. Units:
Since the length and width are in inches, the area will be in square inches.
- Area:
[tex]\[ A = 75 \text{ square inches} \][/tex]
### Summary:
- Perimeter: 40 inches
- Area: 75 square inches
### Finding the Perimeter:
1. Formula for Perimeter of a Rectangle:
The perimeter [tex]\( P \)[/tex] of a rectangle is calculated using the formula:
[tex]\[ P = 2 \times (\text{length} + \text{width}) \][/tex]
2. Substitute the given values:
The length [tex]\( l = 15 \)[/tex] inches, and the width [tex]\( w = 5 \)[/tex] inches. Substitute these values into the formula:
[tex]\[ P = 2 \times (15 + 5) \][/tex]
3. Perform the operations inside the parentheses first:
[tex]\[ 15 + 5 = 20 \][/tex]
4. Multiply the sum by 2:
[tex]\[ P = 2 \times 20 = 40 \][/tex]
5. Units:
Since we're dealing with inches, the perimeter will be in inches.
- Perimeter:
[tex]\[ P = 40 \text{ inches} \][/tex]
### Finding the Area:
1. Formula for Area of a Rectangle:
The area [tex]\( A \)[/tex] of a rectangle is calculated using the formula:
[tex]\[ A = \text{length} \times \text{width} \][/tex]
2. Substitute the given values:
Again, the length [tex]\( l = 15 \)[/tex] inches, and the width [tex]\( w = 5 \)[/tex] inches. Substitute these values into the formula:
[tex]\[ A = 15 \times 5 \][/tex]
3. Multiply the length by the width:
[tex]\[ 15 \times 5 = 75 \][/tex]
4. Units:
Since the length and width are in inches, the area will be in square inches.
- Area:
[tex]\[ A = 75 \text{ square inches} \][/tex]
### Summary:
- Perimeter: 40 inches
- Area: 75 square inches
