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igor_vitrenko [27]
3 years ago
13

45 points + brainliest for correct & explained answer :)

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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