In triangle ABC, angle ABC = 90 degrees, BD is perpendicular to AC, AD = 12 cm, CD = 16 cm

| March 11, 2021 | education

In triangle ABC, angle ABC = 90 degrees, BD is perpendicular to AC, AD = 12 cm, CD = 16 cm, find the lengths of the sides, BC, AB, BD.

In a right-angled triangle ABC, the height BD is drawn from the vertex of the right angle, then the square of its length will be equal to the product of the segments AD and CD, into which the hypotenuse of AC is divided.

BD ^ 2 = AD * CD = 12 * 16 = 192.

ВD = √192 = 8 * √3 cm.

In a right-angled triangle ABD, we apply the Pythagorean theorem and determine the length of the hypotenuse AB.

AB ^ 2 = AD ^ 2 + BD ^ 2 = 144 + 192 = 336.

AB = √336 = 4 * √21 cm.

Determine the length of the AC side. AC = AD + CD = 12 + 16 = 28 cm.

In a right-angled triangle ABC, according to the Pythagorean theorem, we determine the length of the leg BC.

BC ^ 2 = AC ^ 2 – AB ^ 2 = 784 – 336 = 448.

BC = 8 * √7 cm.

Answer: The length of the BC side is 8 * √7 cm, AB is 4 * √21 cm, BD = 8 * √3 cm.



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