To find the perimeter of a rectangle, we use the formula:
\[ \text{Perimeter} = 2 \times (\text{length} + \text{width}) \]
In this case, the length is \(12 \frac{15}{16}\) inches and the width is \(9 \frac{3}{8}\) inches.
First, we convert both mixed numbers to improper fractions:
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Length: \[ 12 \frac{15}{16} = \frac{12 \times 16 + 15}{16} = \frac{192 + 15}{16} = \frac{207}{16} \]
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Width: \[ 9 \frac{3}{8} = \frac{9 \times 8 + 3}{8} = \frac{72 + 3}{8} = \frac{75}{8} \]
Now, we need to add the length and width: To add \(\frac{207}{16}\) and \(\frac{75}{8}\), we need a common denominator, which is 16.
Converting \(\frac{75}{8}\) to a fraction with a denominator of 16: \[ \frac{75}{8} = \frac{75 \times 2}{8 \times 2} = \frac{150}{16} \]
Now add the two fractions: \[ \frac{207}{16} + \frac{150}{16} = \frac{207 + 150}{16} = \frac{357}{16} \]
Now, we can find the perimeter: \[ \text{Perimeter} = 2 \times \left(\frac{357}{16}\right) = \frac{714}{16} \]
To simplify \(\frac{714}{16}\): \[ \frac{714 \div 2}{16 \div 2} = \frac{357}{8} \]
Now we convert \(\frac{357}{8}\) to a mixed number: \[ 357 \div 8 = 44 \text{ remainder } 5 \quad \text{(so it's } 44 \frac{5}{8}\text{)} \]
Therefore, the perimeter of the rectangular poster is \(44 \frac{5}{8}\) inches.
Now let's compare this value with the provided responses:
- 2 3340
- 21 2340
- 43 320
It appears that none of the response options match \(44 \frac{5}{8}\). Perhaps they were intended to show another format of numbers or the options are not related. However, based on the calculation, the perimeter is verified as \(44 \frac{5}{8}\) inches.