In right-angled triangle ABC, ∠C = 90°, and CM is perpendicular to AB. Given AB = 18 cm and BM = 6 cm, find the length of CM.

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Given triangle ABC with right angle at C, and CM perpendicular to hypotenuse AB. We know AB = 18 cm and BM = 6 cm. Since CM is the altitude to the hypotenuse in a right triangle, the following property holds: CM^2 = AM × BM.

First, find AM:
AM = AB - BM = 18 - 6 = 12 cm.

Now, calculate CM:
CM^2 = AM × BM = 12 × 6 = 72
CM = √72 = √(36 × 2) = 6√2 cm.

Therefore, the length of CM is 6√2 cm.

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