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

Question 52

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

Solution

$$25 : x :: x : \frac{81}{4}$$

$$\frac{25}{x}=\ \frac{x}{\frac{81}{4}}$$

$$\frac{25}{x}=\ \frac{4x}{81}$$

$$4x^2\ =\ 25\times81$$

$$x^2\ =\ 25\times\frac{81}{4}$$

$$x^2\ =\ 5^2\times\left(\frac{9}{2}\right)^2$$

$$x = 5\times4.5$$ [Here negative value is not possible. Because it is given that x > 0.]

x = 22.5

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