In a right-angled triangle, the hypotenuse is 10 and one leg is 2 less than the other. Find its area

Let the length of the smaller leg be equal to X cm, AC = X cm, then, by condition, the length of the larger leg BC = 2 * X cm.

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

X ^ 2 + 4 * X ^ 2 = 100.

5 * X ^ 2 = 100.

X ^ 2 = 20.

X = AC = 2 * √5 cm.

Then BC = 4 * √5 cm.

Determine the area of the triangle ABC.

Savs = AC * BC / 2 = 2 * √5 * 4 * √5 / 2 = 4 * 5 = 20 cm2.

Answer: The area of the triangle is 20 cm2.