I don't really understand how to do that
The point about similar triangles is that (1) the measure of any angle in one of the triangles equals the measure of the
corresponding angle in the other triangle, and (2) the
ratios of any
corresponding lengths in the two triangles are identical. So, for example, once you know that triangles DEC and LEK are similar, you also know that
[math]
\dfrac{\text {linear measure of base of } \triangle DEC}{\text {linear measure of base of } \triangle LEK} = \dfrac{\text {linear measure of height of } \triangle DEC}{\text {linear measure of height of } \triangle LEK}.[/math]
With me to here?
Now, the linear measure of the bases are 6 and x respectively, but you do not know what the two heights are. Let’s name them. We say height of DEC is p, and height of LEK is q.
Can we figure out anything about the numerical relationship between those two heights? (A picture will help.)
Yes, we can, namely [imath]p = q + 6.[/imath]
How did we determine that, pray tell?
Therefore, [imath] \dfrac{6}{x} = \dfrac{p}{q} = \dfrac{q + 6}{q}.[/imath]
Now solve for q.