In a right-angled triangle ABC, angle C is 90 degrees, point D is the midpoint of side AB, and point E

In a right-angled triangle ABC, angle C is 90 degrees, point D is the midpoint of side AB, and point E is the midpoint of side BC. DE is 8cm, BE is 6cm. Determine the sides of triangle ABC.

Since, according to the condition, point D is the middle of side AB, and point E is the middle of side BC, then the segment DE is the middle line of the triangle ABC.

Let us determine the length of the AC side through the length of the center line.

Then AC = 2 * DE = 2 * 8 = 16 cm.

Side length BC = 2 * BE = 2 * 6 = 12 cm.

By the Pythagorean theorem, we determine the length of the hypotenuse AB. AB ^ 62 = AC ^ 2 + BC ^ 2 = 16 ^ 2 + 12 ^ 2 = 256 + 144 = 400.

AB = 20 cm.

Answer: The sides of the triangle ABC are 16 cm, 12 cm, 20 cm.