Question

Find the mean proportional of $16$ and $25$.

Answer 1

Step 1: Find the mean proportional

Let, $x$ be the mean proportional of $16$ and $25$.

Now, $16,xand25$ are in continued proportion.

So, $16:x::x:25$

$\Rightarrow \frac{16}{x}=\frac{x}{25}$

$\Rightarrow x\times x=16\times 25$

$\Rightarrow x^2=400$

$\Rightarrow x=\sqrt{400}$

$\Rightarrow x=\pm 20$

Step 2: Consider the positive number

We cannot consider $-20$, because between the two positive numbers, only positive number will lie.

So, the value of $x=20$.

Hence, the mean proportion of $16$ and $25$ is $20$.