Given a right triangle ABC with altitude BD drawn to hypotenuse AC. If AC = 24 and DC = 6, what is the length of BC?

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1. Answer:

   • BC = 12

   Step-by-step explanation:

   BD is the altitude, it breaks ΔABC into two similar triangles:

   • ΔABD ~ ΔBCD

   The ratios of corresponding sides:

   • AD/BD = BD/DC ⇒ BD² = AD*DC ⇒ BD² = (24 – 6)*6 ⇒ BD² = 108

   On the other hand:

   • BC² = BD² + DC² ⇒ BC² = 108 + 6² = 144
   • BC = √144
   • BC = 12

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