Answer:
[tex]BC=71\text{ units}[/tex]
Step-by-step explanation:
Since AD is an altitude, we know that AD⊥BC by the definition of altitudes.
Then, this means that ∠ADC will be 90° by the definition of perpendicular lines. Therefore:
[tex]12x+6=90[/tex]
Solve for x. Subtract 6 from both sides and then divide by 12:
[tex]12x=84\\[/tex]
[tex]x=7[/tex]
Therefore, the value of x is 7.
BC is the addition of the segments BD and DC. In other words:
[tex]BC=BD+DC[/tex]
We already know the equations of BD and DC. Substitute:
[tex]BC=(5x-7)+(2x+29)[/tex]
Since we know that the value of x is 7, substitute 7 for x and evaluate for BC:
[tex]BC=(5(7)-7)+(2(7)+29))[/tex]
Evaluate:
[tex]BC=(35-7)+(14+29)[/tex]
Evaluate:
[tex]BC=28+43=71[/tex]
Therefore, the value of BC is 71 units.
