Answer:
[tex]\large\boxed{5\dfrac{1}{3}\ units}[/tex]
Step-by-step explanation:
ΔZYW and ΔWYX are similar. Therefore corresponding sides are in proportion:
[tex]\dfrac{ZY}{YW}=\dfrac{YW}{YX}[/tex]
We have:
[tex]ZY=3,\ YW=4,\ YX = a[/tex]
Substitute:
[tex]\dfrac{3}{4}=\dfrac{4}{a}[/tex] cross multiply
[tex]3a=(4)(4)[/tex]
[tex]3a=16[/tex] divide both sides by 3
[tex]a=\dfrac{16}{3}\\\\a=5\dfrac{1}{3}[/tex]
