Find the length of the median

Geometry Level pending

In right △ A B C \triangle ABC , B D BD is a median. Given that A B = 24 AB=24 and B C = 18 BC=18 , find the length of B D BD .


The answer is 15.

A Former Brilliant Member by A Former Brilliant Member

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1 solution

In a right triangle, the median from the right vertex to the hypotenuse is equal to half the hypotenuse. Therefore,

B D = 2 4 2 + 1 8 2 2 = 900 2 = 30 2 = 15 BD=\dfrac{\sqrt{24^2+18^2}}{2}=\dfrac{\sqrt{900}}{2}=\dfrac{30}{2}=\boxed{\color{#D61F06}15}

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