If the third proportional of 3x² and 4xy is 48, then the positive value of y is:

Correct option is D

Given:

Third proportional of 3x² and 4xy is 48. Find the positive value of y.

Formula Used:

If a, b, and c are in proportion, then a : b = b : c.

Third proportional, c =  $$\frac{(b²) }{ a}$$​​

Solution:

Let a = 3x², b = 4xy, and c = 48.

Using the formula:

​$$48 = \frac{(4xy)^2}{3x^2} \\[6pt]48 = \frac{16x^2 y^2}{3x^2} \\[6pt]48 = \frac{16}{3} y^2 \\[6pt]y^2 = 48 \times \frac{3}{16} = 9$$​​

y = +3 (positive value)