Applying the altitude theorem and solving algebraically, the length of DC is: 6.
What is the Altitude Theorem?
If an altitude of a right triangle divides an opposite side into a and b, based on the altitude theorem, the height (h) of the altitude = √(ab).
Solving algebraically:
Let DC = x
Therefore:
BC = 4x
Applying the altitude theorem, we would have:
12 = √(4x × x)
12 = √(4x²)
12 = 2x
12/2 = x
6 = x
x = 6
Therefore, DC = x = 6.
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