Calculate Fourth Proportional

To find the fourth proportional of 8, 12, and 4, we use the formula $d = \frac{b \times c}{a}$.

$d = \frac{12 \times 4}{8} = \frac{48}{8} = 6$

Calculate Third Proportional

To find the third proportional of 6 and 9, we use the formula $t = \frac{y^2}{x}$, where $x=6$ and $y=9$.

$t = \frac{9^2}{6} = \frac{81}{6} = 13.5 = \frac{27}{2}$

Find the Ratio

Calculate the ratio of the fourth proportional to the third proportional: $6: 13.5$.

$6: \frac{27}{2} = 12: 27 = 4: 9$