Given right triangle ABCABC with altitude \overline{BD} BD drawn to hypotenuse ACAC. If BC=10BC=10 and DC=5,DC=5, what is the length of \overline{AC}? AC ?

12.5

Step-by-step explanation: The triangle ABC and its altitude is represented in the figure below.

Altitude is a segment of line that link a vertex and the opposite side, forming a right angle.

So, because of , now we have two similar triangles, which means that ratios of corresponding sides are equal:

(1)

This is always true for a right triangle and a altitude drawn to the hypotenuse.

Triangle BDC is also right triangle. So, we can use Pythagorean theorem to determine the missing side.

(2)

Substituting (2) into (1):

We want to find f, so:

f = 7.5

The length of is

The length of the hypotenuse of triangle ABC is 12.5 units.

x = ± 6i

step-by-step explanation:

x^2 = -36

take the square root of each side

sqrt(x^2) = sqrt(-36)

we know sqrt(ab) = sqrt(a) sqrt(b)

x = ±sqrt(36) sqrt(-1)

we know that sqrt (-1) = i

x = ± 6i