If 25 : x :: x : $\frac{81}{4}$, find the value of x, if x > 0.

20.5 22.5 25.0 25.2

22.5

Here, 25 : x :: x : \(\frac{81}{4}\) ⇒ \( { x}^{2 } \) =  25 x \(\frac{81}{4}\) ⇒ x = \(\sqrt {25 × 81/4 }\) ⇒ x = 5 x \(\frac{9}{2}\) ⇒ x = 22.5.