Answer:
[tex]25[/tex].
Step-by-step explanation:
Refer to the diagram attached (not to scale.) Right triangles [tex]\triangle{\sf ADB}[/tex] and [tex]\triangle {\sf BDC}[/tex] are similar triangles because
- Each triangle include a right angle, and
- [tex]\angle {\sf BCD} = 90^{\circ} - \angle {\sf DBC} = \angle {\sf ABD}[/tex].
Hence, the ratio between the length of the corresponding sides would be equal:
[tex]\begin{aligned}\frac{(\sf DC)}{({\sf BD})} = \frac{({\sf BD})}{({\sf AD})}\end{aligned}[/tex].
Given that [tex]({\sf BD}) = 15[/tex] and [tex]({\sf AD}) = 9[/tex], rearrange this equation to find the length of side [tex]({\sf DC})[/tex]:
[tex]\begin{aligned}(\sf DC) &= ({\sf BD})\, \frac{({\sf BD})}{({\sf AD})} \\ &= 15 \times \frac{15}{9} \\ &= 25\end{aligned}[/tex].
In other words, the length of [tex]({\sf DC})[/tex] would be [tex]25[/tex].
