Answer:
[tex]\huge\boxed{x=6}[/tex]
Step-by-step explanation:
[tex]\triangle ABC\ \text{and}\ \triangle ADB\ \text{are similar (AA). Therefore corresponding sides are in proportion.}\\\\\dfrac{BD}{BC}=\dfrac{AB}{AC}\\\\\text{We have}\\\\BD=x\\BC=10\\AB=7.5\\AC=12.5\\\\\text{Subtitute:}\\\\\dfrac{x}{10}=\dfrac{7.5}{12.5}\\\\\dfrac{x}{10}=\dfrac{7.5\cdot10}{12.5\cdot10}\\\\\dfrac{x}{10}=\dfrac{75:25}{125:25}\\\\\dfrac{x}{10}=\dfrac{3}{5}\qquad|\text{cross multiply}\\\\(5)(x)=(3)(10)\\\\5x=30\qquad|\text{divide both sides by 5}\\\\\dfrac{5x}{5}=\dfrac{30}{5}\\\\x=6[/tex]
