One of the legs of a right-angled triangle is equal to 2 root of 6 cm, and the second leg is 2 cm less

One of the legs of a right-angled triangle is equal to 2 root of 6 cm, and the second leg is 2 cm less than the hypotenuse. Find the second leg and hypotenuse of this triangle?

Let the length of the leg BC = X cm, then, by condition, the length of the hypotenuse AB = (X + 2) cm.

By the Pythagorean theorem, in a right-angled triangle ABC:

AB ^ 2 = AC ^ 2 + BC ^ 2.

(X + 2) ^ 2 = (2 * √6) ^ 2 + X ^ 2.

X ^ 2 + 4 * X + 4 = 24 + X ^ 2.

4 * X = 24 – 4 = 20.

X = 20/4 = 5 cm.

BC = 5 cm.

Then AB = 5 + 2 = 7 cm.

Answer: Dean of the hypotenuse is 7 cm, the length of the BC leg is 5 cm.