Given right triangle ABCABC with altitude \overline{BD} BD drawn to hypotenuse ACAC. If AC=16AC=16 and DC=3,DC=3, what is the length of \overline{BC} BC in simplest radical form?

Answer:

4√3

Step-by-step explanation:

Find the diagram attached

Using the similarity theorem of a triangle based on the legs (sides)

AC/BC = BC/DC

Given

AC = 16

DC = 3

Required

BC

Substitute the given values

16/BC = BC/3

Cross multiply

BC² = 16×3

BC² = 48

BC = √48

BC = √16×3

BC = 4√3

Hence the measure of BC is 4√3

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