To find the value of [tex]\( p \)[/tex] in the proportion [tex]\(\frac{20}{6} = \frac{p}{12}\)[/tex], we can use the method of cross-multiplication. Cross-multiplication involves multiplying the numerator of one fraction by the denominator of the other fraction.
1. Multiply the numerator of the left-hand side fraction by the denominator of the right-hand side fraction:
[tex]\[ 20 \times 12 \][/tex]
2. Multiply the denominator of the left-hand side fraction by the numerator of the right-hand side fraction:
[tex]\[ 6 \times p \][/tex]
3. Set the two products equal to each other:
[tex]\[ 20 \times 12 = 6 \times p \][/tex]
4. Calculate the product on the left-hand side:
[tex]\[ 240 = 6 \times p \][/tex]
5. To solve for [tex]\( p \)[/tex], divide both sides of the equation by 6:
[tex]\[ p = \frac{240}{6} \][/tex]
6. Perform the division:
[tex]\[ p = 40.0 \][/tex]
Therefore, the value of [tex]\( p \)[/tex] is 40. Thus, the correct answer is:
40
