In a rectangular triple grip CBA, the angle C is 90 degrees. On the side of AC, point E is taken from

| July 2, 2021 | education

In a rectangular triple grip CBA, the angle C is 90 degrees. On the side of AC, point E is taken from it, the perpendicular EK is lowered to the side AB. BC = 12cm, AE = 10cm, EK = 6cm.Find AB and CD.

Since EK is perpendicular to AB, then the triangle AEK is rectangular, then, according to the Pythagorean theorem, we determine the length of the leg AK. AK ^ 2 = AE ^ 2 – EK ^ 2 = 100 – 36 = 64.

AK = 8 cm.

In right-angled triangles ABC and AEK, the angle A is common, then these triangles are similar in acute angle. Let the length of the segment EC = X cm, then AC = (10 + X) cm.

Then AK / EK = AC / BC.

8/6 = (10 + X) / 12.

96 = 60 + 6 * H.

X = 36/6 = 6 cm.

CE = 6 cm, then AC = 10 + 6 = 16 cm.

Let us determine the length of the hypotenuse AB of the triangle ABC.

AB ^ 2 = AC ^ 2 + BC ^ 2 = 265 + 144 = 400.

AB = 20 cm.

Triangles AEK and ACD are similar in acute angle, then AC / CD = AE / EK.

CD = AC * EK / AE = 16 * 6/10 = 9.6 cm.

Answer: Length AB is 20 cm, CD is 9.6 cm, CE is 6 cm.



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