Final answer:
After cross-multiplication and simplification to solve the given proportion, we find that the value of x is approximately 20.78, which does not match any of the provided answer choices. So, none of the given options are correct.
Step-by-step explanation:
To solve for the value of x in the given proportion 3x/12 = 108/x, we need to cross-multiply.
This means multiplying the numerator of one fraction by the denominator of the other fraction on both sides, which gives us:
3x × x = 108 × 12
Now simplifying, we get:
3x² = 1296
Divide both sides of the equation by 3 to isolate x²:
x^2 = 432
Now take the square root of both sides to solve for x:
x = √432
Which simplifies to:
x = 20.78
However, none of the provided options (a, b, c, d) match this answer.
A proportion is a mathematical equation that states that two ratios or fractions are equal.
Proportions are often used to solve problems involving ratios and relationships between quantities.