Given right triangle A B C with altitude overline{B D} drawn to hypotenuse overline{A C}. If A B=10 and A D=5, what is the length of overline{A C} ?

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Step:1 ：Given right triangle ABC with altitude BD drawn to the hypotenuse AC, we have AB = 10 and AD = 5. Using similar triangles ABD and ABC, we get the ratio AB/AD = AC/AB, which simplifies to AC = 20.Step:2 ：Now, using the Pythagorean theorem, we have AB^2 + BC^2 = AC^2. Plugging in the values, we get 10^2 + BC^2 = 20^2. Solving for BC, we find BC = ( sqrt{20^2 - 10^2} ) = 17.32 (approx).Step:3 ：( boxed{AC = 20} )

Answer

Step: 1 ：Given right triangle ABC with altitude BD drawn to the hypotenuse AC, we have AB = 10 and AD = 5. Using similar triangles ABD and ABC, we get the ratio AB/AD = AC/AB, which simplifies to AC = 20.Step: 2 ：Now, using the Pythagorean theorem, we have AB^2 + BC^2 = AC^2. Plugging in the values, we get 10^2 + BC^2 = 20^2. Solving for BC, we find BC = ( sqrt{20^2 - 10^2} ) = 17.32 (approx).Step: 3 ：( boxed{AC = 20} )

Given right triangle $A B C$ with altitude $\overline{B D}$ drawn to hypotenuse $\overline{A C}$. If $A B=10$ and $A D=5$, what is the length of $\overline{A C}$ ?

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