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Given right triangle ABC with altitude BD drawn to hypotenuse AC. If AC=19 and DC=5, what is the length of BC in simplest radical form? (Note: the figure is not drawn to scale.)

 Sep 5, 2021
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Ok, so I think the answer is the square root of 70. Based on the information I drew out a picture. Then I made two equations: 5^2 + x^2 = a^2 and 14^2 + x^2 = b^2. Because triangles ABD and CBD are right triangles I used the Pythagorean theorem to create those two equations. Then I can add a^2 and b^2 together to get c^2. So, I add both equations together: 5^2+x^2 + x^2 +14^2 = 19^2. Then solving the equation: 5^2 + 14^2 + 2x^2 = 19^2. I end up with x^2 = 70 which is the square root of 70. I hope this helps! 

 Sep 5, 2021

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