Question

Given right triangle ABCABC with altitude \overline{BD} BD drawn to hypotenuse ACAC. If AC=12AC=12 and BC=6,BC=6, what is the length of \overline{DC}? DC ?

Answer 1

AC. BD. 2 In the accompanying diagram of right triangle ABC, altitude BD is drawn to ... BD. AC. 3 In the diagram below, the length of the legs AC and. BC of right triangle ABC are 6 cm and 8 cm, ... BC. If BD = 2 and DC = 10, what is the length of AB? ... hypotenuse RS. If RV = 12 and RT = 18, what is the length of SV? 1) 6 5.

Answer 2

Using Pythagorean theorem in solving, and considering the given triangle, the length of DC is 12√3.

How is that so?

Step 1: Find the length of the other leg (AB) using the Pythagorean Theorem.

Since we know AC = 12 and BC = 6, we can use the Pythagorean Theorem to find the length of the other leg, AB:

AB² = AC² - BC²

AB² = 12² - 6²

AB² = 144 - 36

AB² = 108

AB = √108

AB = 6√3

Step 2: Use similar triangles to find the length of DC.

Triangles BCD and ABC are similar right triangles due to the altitude BD being drawn perpendicular to the hypotenuse AC. Therefore, we can set up a proportion relating the corresponding sides of the two triangles:

BC/DC = AB/AC

6/DC = 6√3 / 12

Step 3: Solve for DC.

Cross-multiply and solve for DC:

6 * DC = 6√3 * 12

DC = (6√3 * 12) / 6

DC = 6 * √3 * 2

DC = 12√3

Therefore, the length of DC is 12√3.