Respuesta :

Answer:

  • 18

Step-by-step explanation:

By similar triangles law:-

[tex]\frac{24}{2x} =\frac{30}{x+6}[/tex]

[tex]24(x+6)=30(2x)[/tex]

[tex]24x+24(6)=60x[/tex]

[tex]24x+144=60x[/tex]

[tex]\frac{36x}{36x} =\frac{144}{36}[/tex]

[tex]x=4[/tex]

Since AB=x+6+2x

[tex]AB=3x+6[/tex]

Substitute value of x

[tex]AB=3(4)+6[/tex]

[tex]AB=12+6[/tex]

[tex]AB=18[/tex]

Therefore, the third side of ΔABC is 18.

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Hope this helps!