Answer :
To find the length of the rectangle, let's use the formula for the perimeter of a rectangle:
The formula for the perimeter [tex]\( P \)[/tex] of a rectangle is:
[tex]\[ P = 2 \times (\text{length} + \text{width}) \][/tex]
We are given:
- The width of the rectangle is 46 centimeters.
- The perimeter of the rectangle is 186 centimeters.
Let's plug these values into the perimeter formula:
[tex]\[ 186 = 2 \times (\text{length} + 46) \][/tex]
To find the length, first simplify the equation:
[tex]\[ 186 = 2 \times \text{length} + 92 \][/tex]
Now, subtract 92 from both sides to isolate the term with the length:
[tex]\[ 186 - 92 = 2 \times \text{length} \][/tex]
[tex]\[ 94 = 2 \times \text{length} \][/tex]
Next, divide both sides by 2 to solve for the length:
[tex]\[ \text{length} = \frac{94}{2} \][/tex]
[tex]\[ \text{length} = 47 \][/tex]
Therefore, the length of the rectangle is 47 centimeters.
The formula for the perimeter [tex]\( P \)[/tex] of a rectangle is:
[tex]\[ P = 2 \times (\text{length} + \text{width}) \][/tex]
We are given:
- The width of the rectangle is 46 centimeters.
- The perimeter of the rectangle is 186 centimeters.
Let's plug these values into the perimeter formula:
[tex]\[ 186 = 2 \times (\text{length} + 46) \][/tex]
To find the length, first simplify the equation:
[tex]\[ 186 = 2 \times \text{length} + 92 \][/tex]
Now, subtract 92 from both sides to isolate the term with the length:
[tex]\[ 186 - 92 = 2 \times \text{length} \][/tex]
[tex]\[ 94 = 2 \times \text{length} \][/tex]
Next, divide both sides by 2 to solve for the length:
[tex]\[ \text{length} = \frac{94}{2} \][/tex]
[tex]\[ \text{length} = 47 \][/tex]
Therefore, the length of the rectangle is 47 centimeters.
