The third proportional to 38 and 15 is :

1. $\dfrac{15}{38 \times 38}$

2. $\dfrac{38 \times 38}{15}$

3. $\dfrac{15 \times 15}{38}$

4. $\dfrac{38 \times 15}{2}$

Let third proportional be x.

⇒ 38 : 15 = 15 : x

⇒ $\dfrac{38}{15} = \dfrac{15}{x}$

⇒ 38x = 15 × 15

⇒ x = $\dfrac{15 \times 15}{38}$

Hence, option 3 is the correct option.