Solution:
Given:
[tex]\frac{2ft\text{ }9in}{4ft\text{ }7in}=\frac{2.4cm}{x}[/tex]To solve for x, we take the units to the same quantity.
Converting all units to centimeters,
[tex]\begin{gathered} 1ft=30.48cm \\ 1in=2.54cm \\ \\ Hence, \\ 2ft\text{ }9in=2(30.48)+9(2.54)=60.96+22.86 \\ 2ft\text{ }9in=83.82cm \\ \\ \\ Also, \\ 4ft\text{ }7in=4(30.48)+7(2.54)=121.92+17.78 \\ 4ft\text{ }7in=139.7cm \end{gathered}[/tex]Hence:
[tex]\begin{gathered} \frac{2ft\text{ }9in}{4ft\text{ }7in}=\frac{2.4cm}{x} \\ \frac{83.82cm}{139.7cm}=\frac{2.4cm}{x} \\ \\ Cross\text{ multiplying the equation:} \\ 83.82\times x=139.7\times2.4 \\ x=\frac{139.7\times2.4}{83.82} \\ x=\frac{335.28}{83.82} \\ x=4cm \end{gathered}[/tex]
Therefore, x = 4cm