In a right triangle ABC, BD is perpendicular on hypotenuse AC. If AC=9 cm and AD=4 cm, then what is AB+BC approximately equal to?

Explanation

By geometric mean theorems, AB = \sqrt{AD \times AC} = \sqrt{4 \times 9} = 6 cm. The segment CD = AC - AD = 9 - 4 = 5 cm. BC = \sqrt{CD \times AC} = \sqrt{5 \times 9} = \sqrt{45} \approx 6.708 cm. Therefore, AB + BC \approx 6 + 6.708 = 12.708 cm, closest to 12.6 cm.

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