One leg of a right-angled triangle is 3 times larger than the other. the hypotenuse is 2√10. find a smaller leg.

Let the length of one leg be x. Then, from the condition of the problem, we know that the second is 3 times larger than the other, we get 3 * x.
By the Pythagorean theorem, the sum of the squares of the legs is equal to the square of the hypothesis.
We know that the hypotenuse is 2√10.
Thus, we get the equation:
x ^ 2 + (3 * x) ^ 2 = (2√10) ^ 2
x ^ 2 + 3 ^ 2 * x ^ 2 = 2 ^ 2 * (√10) ^ 2
x ^ 2 + 9 * x ^ 2 = 4 * 10
x ^ 2 * (1 + 9) = 4 * 10
x ^ 2 * 10 = 4 * 10
x ^ 2 = 4
x = √4
x = 2

Thus, we get that the smallest leg of a right-angled triangle will be equal to 2.

Answer: 2