A perpendicular KC is drawn through the vertex of the right angle C to the plane of the right-angled triangle ABC
A perpendicular KC is drawn through the vertex of the right angle C to the plane of the right-angled triangle ABC. Point D bisects the hypotenuse AB. The length of the legs of the triangle is AC = 96 mm and BC = 128 mm. Distance KC = 84 mm. Determine the length of the segment KD.
In a right-angled triangle ABC, on the Pythagorean theorem, we determine the length of the hypotenuse AB.
AB ^ 2 = AC ^ 2 + BC ^ 2 = 9216 + 16384 = 25600.
AB = 160 cm.
According to the condition, point D is the middle of the hypotenuse of blood pressure, then the segment of СD is a median drawn from the top of the right angle, the length of which is equal to half the length of the hypotenuse.
СD = AD / 2 = 160/2 = 80 cm.
The desired segment of the CD is the hypotenuse of the right-angled triangle СKD, then CD ^ 2 = СK ^ 2 + СD ^ 2 = 7056 + 6400 = 13456.
КD = 116 cm.
Answer: The length of the CD segment is 116 cm.
