Triangle ABC CD perpendicular to AB angle C = 90 degrees AC = 5 cm AB = 13 cm find CB, CD, BD, AD.

univerkov | May 26, 2021 | education

Since the triangle ABC is rectangular, then by the Pythagorean theorem we determine the length of the leg BC.

BC ^ 2 = AB ^ 2 – AC ^ 2 = 169 – 25 = 144.

BC = 12 cm.

Determine the area of the triangle ABC. Savs = AC * BC / 2 = 5 * 12/2 = 30 cm2.

Also Savs = AB * CD / 2.

СD = 2 * Saс / AB = 2 * 30/13 = 60/13 = 4 (8/13) cm.

In a right-angled triangle ACD, according to the Pythagorean theorem, AD ^ 2 = AC ^ 2 – CD ^ 2 = 25 – 3600/169 = 625/169.

AD = 25/13 = 1 (12/13).

BD = AB – AD = 13 – 25/13 = 144/13 = 11 (1/13) cm.

Answer: CB = 12 cm, CD = 4 (8/13) cm, BD = 11 (1/3) cm, AD = 1 (12/13) cm.

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