###### Example3.7.7

Since the two triangles are similar, we know that their side length should be proportional. To determine the unknown length, we can set up a proportion and solve for $$x\text{:}$$

\begin{align*} \frac{\text{bigger triangle's left side length in cm}}{\text{bigger triangle's bottom side length in cm}}\amp=\frac{\text{smaller triangle's left side length in cm}}{\text{smaller triangle's bottom side length in cm}}\\ \frac{x\,\text{cm}}{6\,\text{cm}}\amp=\frac{3\,\text{cm}}{4\,\text{cm}}\\ \frac{x}{6}\amp=\frac{3}{4}\\ \multiplyleft{12}\frac{x}{6}\amp=\multiplyleft{12}\frac{3}{4}\qquad\text{(12 is the least common denominator)}\\ 2x\amp=9\\ \divideunder{2x}{2}\amp=\divideunder{9}{2}\\ x\amp=\frac{9}{2}\ \text{or}\ 4.5 \end{align*}

The unknown side length is then 4.5 cm.

in-context