Question

The third proportional of a and $\frac{b^4}{4a}$ is

• A. $$\frac{{{b^8}}}{{16{a^2}}}$$
• B. $$\frac{{{b^8}}}{{8{a^2}}}$$
• C. $$\frac{{{b^8}}}{{8{a^3}}}$$
• D. $$\frac{{{b^8}}}{{16{a^3}}}$$

Answer 1

Answer:

$$\frac{{{b^8}}}{{16{a^3}}}$$

Solution:

Given  :

The third proportional of a and 

Formula:

If x, y, and z are in proportion

$\large{x\over y} = {y\over z}$

⇒ y² = xz

Calculation:

Let the third proportional to a and $\large\frac{{{b^4}}}{{4a}}$ be x

According to the question $a :\frac{b^4}{4a}::\frac{b^4}{4a}:x$

$x=\frac{\frac{b^4}{4a}\times{\frac{b^4}{4a}}}{a}$

$x=\frac{b^3}{16a^3}$

Hence, 'Option 4' is correct answer.