To compute the length of a rectangle when given the perimeter and the width, we need to use the formula for the perimeter of a rectangle.
The perimeter (P) of a rectangle is given by the formula:
[tex]\[ P = 2 \times ( \text{length} + \text{width} ) \][/tex]
Given:
[tex]\[ P = 40.2 \text{ inches} \][/tex]
[tex]\[ \text{width} = 6.7 \text{ inches} \][/tex]
We need to find the length (L) of the rectangle.
First, start with the perimeter formula and solve for the length:
[tex]\[ 40.2 = 2 \times (\text{length} + 6.7) \][/tex]
Divide both sides by 2 to isolate the term involving the length:
[tex]\[ \frac{40.2}{2} = \text{length} + 6.7 \][/tex]
[tex]\[ 20.1 = \text{length} + 6.7 \][/tex]
Next, subtract the width from both sides to solve for the length:
[tex]\[ 20.1 - 6.7 = \text{length} \][/tex]
[tex]\[ \text{length} = 13.4 \text{ inches} \][/tex]
Therefore, the length of the rectangle is 13.4 inches.
