Question

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

• A. 6
• B. 2
• C. 9
• D. 3

Answer 1

Answer:

D. 3

For numbers (a, b, c) in third proportional:
$\frac{a}{b} = \frac{b}{c} ;\Rightarrow; c = \frac{b^2}{a}$

Here,
$(a = 3x^2), (b = 4xy),$ and third proportional $(c = 48)$

$48 = \frac{(4xy)^2}{3x^2}$

$48 = \frac{16x^2y^2}{3x^2}$

Cancel $(x^2):$
$48 = \frac{16y^2}{3}$

$48 \times 3 = 16y^2$
$\Rightarrow 144 = 16y^2$
$y^2 = 9$
$\Rightarrow y = \pm 3$

Since positive value is required:

Final Answer:

y = 3