Lets draw a picture:
We can see that triangle ABC and triangle BCD are similar. Then the following ration must be preserve:
[tex] \frac{short \: leg \: (medium)}{hypotenuse \: (med)} = \frac{short \: leg \: (large)}{hypotenuse \: (large)} [/tex]
Which gives:
[tex] \frac{x}{18} = \frac{24}{30} [/tex]
If we move 18 to the right hand side, we get
[tex]x = 18 \: \frac{24}{30} [/tex]
Which gives:
[tex]x = \: \frac{432}{30} \\ x = 14.4[/tex]
Then, x is equal to 14.4 units.
