Since we have that BD is the median, it divides the segment or side of the triangle into two equal parts. Then, we have that:
[tex]AD=CD\Rightarrow6x+10=2x+12[/tex]
Then, we need to solve the equation for x, and to do so, we need to:
1. Subtract 2x, and 10 from both equations:
[tex]6x-2x+10-10=2x-2x+12-10\Rightarrow6x-2x=12-10[/tex]
2. Since we have like terms, then we have:
[tex]6x-2x=12-10\Rightarrow4x=2\Rightarrow\frac{4}{4}x=\frac{2}{4}\Rightarrow x=\frac{2}{4}\Rightarrow x=\frac{1}{2}[/tex]
In the previous step, we divide both sides of the equation by 4 and then simplify the resulting fraction.
Hence, the value for x = 1/2. The length of AC is the sum of AD + CD or twice the value of one of them:
[tex]AD+CD=6x+10+2x+12=6\cdot\frac{1}{2}+10+2\cdot\frac{1}{2}+12=\frac{6}{2}+10+\frac{2}{2}+12[/tex]
Therefore, the length of AC is
[tex]AC=3+10+1+12\Rightarrow AC=26[/tex]
AC = 26 units.
