Answer:
CX = 3.2 cm
Step-by-step explanation:
We can find the length of CX by comparing the ΔABX and ΔABC. Refer to the attached picture, we can see that 2 pairs of the corresponding angles are equal (∠CAB = ∠AXB = 90° and ∠CBA = ∠ABX).
Therefore based on the triangle similarity theorem, ΔABX and ΔABC are similar triangles, which means:
[tex]\boxed{AC:XA=AB:XB=BC:BA}[/tex]
Using the Pythagorean theorem for ΔABC:
[tex]BC^2=AB^2+AC^2[/tex]
[tex]BC^2=3^2+4^2[/tex]
[tex]BC=\sqrt{25}[/tex]
[tex]BC=5\ cm[/tex]
[tex]AB:BC=XB:AB[/tex]
[tex]3:5=XB:3[/tex]
[tex]XB=3\times3\div5[/tex]
[tex]XB=1.8\ cm[/tex]
[tex]BC=XB+CX[/tex]
[tex]5=1.8+CX[/tex]
[tex]CX=5-1.8[/tex]
[tex]\bf CX=3.2\ cm[/tex]
