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Mathematics

1 answer:

devlian [24]3 years ago

7 0

|AD| = 30 - 6 = 24

The triangle ABC and the triangle BDA are similar, therefore:

$\dfrac{30}{x}=\dfrac{x}{24}\ \ \ \ |cross\ multiply\\\\x^2=30\cdot24\to x=\sqrt{30\cdot24}\\\\x=\sqrt{5\cdot6\cdot6\cdot4}\\\\x=\sqrt{6^2\cdot4\cdot5}\\\\x=\sqrt{6^2}\cdot\sqrt4\cdot\sqrt5\\\\x=6\cdot2\cdot5\\\\\boxed{x=12\sqrt5}$

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