To find the other side of the rectangle, we follow these steps:
1. Convert the mixed numbers to improper fractions for easier calculations.
- The area of the rectangle is given as [tex]\(45 \frac{5}{16} \, \text{cm}^2\)[/tex].
- Convert [tex]\(45 \frac{5}{16}\)[/tex] to an improper fraction:
[tex]\[
45 \frac{5}{16} = \frac{45 \times 16 + 5}{16} = \frac{720 + 5}{16} = \frac{725}{16} \, \text{cm}^2
\][/tex]
- The length of one edge is given as [tex]\(6 \frac{1}{4} \, \text{cm}\)[/tex].
- Convert [tex]\(6 \frac{1}{4}\)[/tex] to an improper fraction:
[tex]\[
6 \frac{1}{4} = \frac{6 \times 4 + 1}{4} = \frac{24 + 1}{4} = \frac{25}{4} \, \text{cm}
\][/tex]
2. Set up the formula for the area of a rectangle:
[tex]\[
\text{Area} = \text{Length} \times \text{Width}
\][/tex]
- In this situation, we need to find the width given the area and one length:
[tex]\[
\text{Width} = \frac{\text{Area}}{\text{Length}}
\][/tex]
3. Substitute the given values into the formula:
- Substitute the area ([tex]\(\frac{725}{16}\)[/tex]) and the known side ([tex]\(\frac{25}{4}\)[/tex]) into the formula:
[tex]\[
\text{Width} = \frac{\frac{725}{16}}{\frac{25}{4}}
\][/tex]
4. Simplify the expression:
- Division by a fraction is equivalent to multiplication by its reciprocal:
[tex]\[
\text{Width} = \frac{725}{16} \times \frac{4}{25}
\][/tex]
- Multiply the numerators and the denominators:
[tex]\[
\text{Width} = \frac{725 \times 4}{16 \times 25} = \frac{2900}{400}
\][/tex]
- Simplify [tex]\(\frac{2900}{400}\)[/tex]:
[tex]\[
\frac{2900}{400} = 7.25 \, \text{cm}
\][/tex]
So, the other side of the rectangle is [tex]\(7.25 \, \text{cm}\)[/tex].
