In a right-angled triangle, one of the legs is 50% of the other leg. Find the legs of the triangle

In a right-angled triangle, one of the legs is 50% of the other leg. Find the legs of the triangle if the hypotenuse is 3V5 cm.

Let the length of the smaller leg be X cm, BC = X cm, then, by condition, the length of the larger leg is 2 * X cm, AB = 2 * X cm.

By the Pythagorean theorem, AC ^ 2 = AB ^ 2 + BC ^ 2.

(3 * √5) ^ 2 = X ^ 2 + (2 * X) ^ 2.

45 = 5 * X ^ 2.

X ^ 2 = 45/5 = 9.

X = BC = 3 cm.

AB = 2 * 3 = 6 cm.

Answer: The lengths of the legs are 3 cm and 6 cm.