The fourth proportional to 4, a and 16a is 81. Find the value of a².

Correct option is A

Given:

Fourth proportional to 4, a, and 16a is 81

That is, $$\frac{4}{a} = \frac{16a}{81}$$​​

Concept Used:

If a : b = c : d, then d is the fourth proportional to a, b, c

Solution:​

​$$\frac{4}{a} = \frac{16a}{81} \\ \ \\\Rightarrow 4 \times 81 = a \times 16a \\ \ \\\Rightarrow 324 = 16a^2 \\ \ \\\Rightarrow a^2 = \frac{324}{16} = 20.25$$​​