Answer:
[tex]AC=5[/tex]
Step-by-step explanation:
From the question we are told that:
Dimensions
[tex]AD=4\\BD=6[/tex]
Generally the equation for these similar right triangle is mathematically given by
[tex]\frac{AC}{AB}=\frac{AB}{AD}=\frac{BC}{BD}[/tex]
[tex]\frac{AC}{AB}=\frac{AB}{AD}[/tex]
Where
[tex]AD=x[/tex]
[tex]AC=x+4[/tex]
Therefore
[tex]AB^2=x(x+4)[/tex]
Generally the Pythagoras equation for [tex]\triangle[/tex]ADB is mathematically given by
[tex]AB^2=BD^2+AD^2[/tex]
[tex]x(x+4)=4+x^2[/tex]
[tex]x(x+4)-(4+x^2)=0[/tex]
[tex]x^2+4x)-(4+x^2)=0[/tex]
[tex]4x-4=0[/tex]
[tex]x=1[/tex]
Therefore
[tex]AC=x+4[/tex]
[tex]AC=1+4[/tex]
[tex]AC=5[/tex]
