# In a right triangle ABC, CD is an altitude, such that AD=BC. Find AC, if AB=3 cm, and CD= 2 cm.

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## Question:

In a right triangle ABC, CD is an altitude, such that AD=BC. Find AC, if AB=3 cm, and CD= 2 cm.

Consider right triangle ΔABC with legs AC and BC and hypotenuse AB. Draw the altitude CD.

1. Theorem: The length of each leg of a right triangle is the geometric mean of the length of the hypotenuse and the length of the segment of the hypotenuse adjacent to that leg.

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According to this theorem, Let BC=x cm, then AD=BC=x cm and BD=AB-AD=3-x cm. Then Take positive value x. You get 2. According to the previous theorem, Then Answer: This solution doesn’t need CD=2 cm. Note that if AB=3cm and CD=2cm, then This means that you cannot find solutions of this equation. Then CD≠2 cm.

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