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Question

If \frac{2a}{3}=\frac{4b}{5}=\frac{3c}{4}
, then what is the value of \frac{18}{a}\sqrt{a^2+c^2-b^2}
?

  1. 3\sqrt{5}
  2. \sqrt{355}
  3. \sqrt{375}
  4. 3\sqrt{15}
Answer

Let \frac{2a}{3}=\frac{4b}{5}=\frac{3c}{4}=k

a=\frac{3k}{2}, b=\frac{5k}{4},c=\frac{4k}{3}

\frac{18\times2}{3k}\sqrt{\frac{9k^2}{4}+\frac{16k^2}{9}-\frac{25k^2}{16}}

\frac{18\times2}{3k}\sqrt{\frac{324k^2+256k^2-225k^2}{144}}

\sqrt{355}

Answer (B) – \sqrt{355}

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