Question

Triangle KAB is similar to triangle KML. Find the length of AB.L36B5430K50A

Answer 1

Given the figure in the attached image;

The triangles KAB and KML are similar

$\Delta KAB\text{ \textasciitilde}\Delta KML$

So, the sides of the triangles are proportional.

$\frac{KB}{KL}=\frac{AB}{ML}$

Given in the figure;

$\begin{gathered} KB=30 \\ KL=36 \\ ML=54 \end{gathered}$

substituting the given values;

$\begin{gathered} \frac{KB}{KL}=\frac{AB}{ML} \\ \frac{30}{36}=\frac{AB}{54} \\ AB=\frac{30\times54}{36} \\ AB=45 \end{gathered}$

Therefore, the length of side AB is;

$45\text{ units}$