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

Question

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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Kim Cúc 1 year 2021-08-31T15:12:37+00:00 1 Answers 0 views 0

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    2021-08-31T15:14:33+00:00

    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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