Find b if 256, b and 324 are in continued proportion.

Correct option is D

Given

Three numbers 256, b, and 324 are in continued proportion.

Concept Used

In continued proportion, the square of the middle term (b) equals the product of the first and third terms:

​$$b^2 = a \cdot c$$​​

Solution

Substituting a = 256 and c = 324:

b = $$\sqrt{256 \cdot 324}$$​ ​

b = $$\sqrt{16 \times 16 \times 18 \times 18 }$$​​

b = $$16 \times 18$$​​

b = 288