Question

Given right triangle ABC with altitude BD drawn to hypotenuse AC. If AD = 9 and

BD = 12, what is the length of DC?
A
Answer Attempt 2 out of a
DC =
B
12
D
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10:52 PM

Answer 1

Using the Pythagorean theorem, we can find that the length of DC is 6 units.

Step-by-step explanation:

To find the length of DC in right triangle ABC with altitude BD drawn to hypotenuse AC, we can use the Pythagorean theorem. In our triangle, AD and BD are the legs, and AC will be the hypotenuse. Since we are given that AD = 9 and BD = 12, we can set up an equation as follows:

AD² + BD² = AC²

9² + 12² = AC²

81 + 144 = AC²

225 = AC²

AC = √225

AC = 15

Now, to find DC, we subtract the length of AD from AC:

DC = AC - AD

DC = 15 - 9

DC = 6

Thus, the length of DC is 6 units.