Given: 144 : x : : x : 121

To find the value of x, we need to understand the relationship between 144, x, and 121.

The given expression can be rewritten as a proportion:

144/x = x/121

To solve for x, we can cross-multiply:

144 * 121 = x * x

17424 = x^2

Taking the square root of both sides, we get:

x = √17424

x ≈ 132

Therefore, the value of x is approximately 132.

Explanation:
To solve this question, we can use the concept of proportions. Proportions express the equality of two ratios. In this case, we have the proportion:

144/x = x/121

We can interpret this proportion as saying that the ratio of 144 to x is equal to the ratio of x to 121. In other words, the two ratios are equivalent.

To solve for x, we can cross-multiply the proportion. Cross-multiplying means multiplying the numerator of the first ratio by the denominator of the second ratio, and vice versa. This gives us:

144 * 121 = x * x

Simplifying the equation, we get:

17424 = x^2

To isolate x, we need to take the square root of both sides of the equation. The square root of x^2 is x, so we have:

x = √17424

Using a calculator, we find that the square root of 17424 is approximately 132.

Therefore, the value of x is approximately 132, which corresponds to option C.

144 : x :: x : 121
x^2 = 144*121
x = 132