To find the perimeter of a rectangle, you use the formula:
[tex]\[ P = 2 \times (\text{length} + \text{width}) \][/tex]
A rectangle has 4 sides.
Let's simplify the length and width of the rectangle step-by-step.
Length Simplification:
Given: [tex]\( 5(x - 3) \)[/tex]
First, distribute the 5:
[tex]\[ 5(x - 3) = 5x - 15 \][/tex]
So, the length of the rectangle simplifies to:
[tex]\[ 5x - 15 \][/tex]
Width Simplification:
Given: [tex]\(\frac{1}{3}(3x + 15)\)[/tex]
First, distribute the [tex]\(\frac{1}{3}\)[/tex]:
[tex]\[ \frac{1}{3}(3x + 15) = \frac{1}{3} \times 3x + \frac{1}{3} \times 15 \][/tex]
Calculate each term:
[tex]\[ \frac{1}{3} \times 3x = x \][/tex]
[tex]\[ \frac{1}{3} \times 15 = 5 \][/tex]
So, the width of the rectangle simplifies to:
[tex]\[ x + 5 \][/tex]
Calculating the Perimeter:
Now that we have the simplified length and width, we can calculate the perimeter:
[tex]\[ \text{Length} = 5x - 15 \][/tex]
[tex]\[ \text{Width} = x + 5 \][/tex]
Substituting these into the perimeter formula:
[tex]\[ P = 2 \times (5x - 15 + x + 5) \][/tex]
Combine like terms inside the parentheses:
[tex]\[ P = 2 \times (6x - 10) \][/tex]
Distribute the 2:
[tex]\[ P = 12x - 20 \][/tex]
So, the perimeter of the rectangle simplifies to:
[tex]\[ 12x - 20 \][/tex]
Finally, summarizing the simplified values:
- The length of the rectangle is [tex]\( 5x - 15 \)[/tex]
- The width of the rectangle is [tex]\( x + 5 \)[/tex]
- The perimeter of the rectangle is [tex]\( 12x - 20 \)[/tex]
- The rectangle has 4 sides.
