Find the sides of a right-angled isosceles triangle if its hypotenuse is 3√2 cm.

To solve this problem, you need to use the Pythagorean theorem. According to this theorem, the following equality is true in a right-angled triangle:

c² = a² + b², where c is the hypotenuse of the triangle, a and b are its legs.

This triangle is isosceles and therefore a = b. Hence, the previous theorem can be written as follows:

c² = 2a².

Let us express the leg from this formula:

a = c / √2.

We know the hypotenuse, which means we can find the leg. Let’s calculate its length:

a = 3√2 / √2 = 3 cm.

Answer: the sides of a right-angled isosceles triangle are 3 cm.