In a right-angled triangle ABC, angle C 90 AC 6 cm BC = 8 cm bisector CK = 10 cm

univerkov | July 16, 2021 | education

In a right-angled triangle ABC, angle C 90 AC 6 cm BC = 8 cm bisector CK = 10 cm Find the perimeter of the triangle CKB.

By the Pythagorean theorem, we determine the length of the hypotenuse AB.

AB ^ 2 = BC ^ 2 + AC ^ 2 = 64 + 36 = 100.

AB = 10 cm.

Let the length of the segment BK = X cm, then AK = (10 – X) cm.

By the property of the bisector of a triangle: BC / BK = AC / AK.

8 / X = 6 / (10 – X).

6 * X = 80 – 8 * X.

14 * X = 80.

X = BK = 80/14 = 5 (5/7) cm.

Then Rskv = BC + CK + BK = 8 + 10 + 5 (5/7) = 23 (5/7) cm.

Answer: The perimeter of the triangle CKB is 23 (5/7) cm.

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