Question

Solve the proportion.
r

24
=
6

3
r

Answer 1

To solve the proportion

\[
\frac{r}{24} = \frac{6}{3r}
\]

we can cross-multiply:

\[
r \cdot 3r = 6 \cdot 24
\]

This simplifies to:

\[
3r^2 = 144
\]

Next, divide both sides by 3:

\[
r^2 = 48
\]

Now, take the square root of both sides:

\[
r = \sqrt{48}
\]

We can simplify \(\sqrt{48}\):

\[
\sqrt{48} = \sqrt{16 \cdot 3} = \sqrt{16} \cdot \sqrt{3} = 4\sqrt{3}
\]

Thus, the solution for \(r\) is:

\[
r = 4\sqrt{3}
\]