In a right-angled isosceles triangle, the hypotenuse is 4√2 cm. Find the side of the triangle.

In a right-angled triangle, a and b are legs, c is hypotenuse.

Let’s solve the problem by the Pythagorean theorem:

The square of the hypotenuse is equal to the sum of the squares of the legs.

c ^ 2 = a ^ 2 + b ^ 2;

By the condition of the problem, the triangle is isosceles, the sides are equal:

a = b, we get

c ^ 2 = 2 × a ^ 2.

Let’s find what is equal to a

a ^ 2 = c 2: 2.

Substitute in the resulting equation the value c = 4√2 cm

a ^ 2 = (4√2) ^ 2: 2;

a ^ 2 = 16 × 2: 2;

a = √16;

a = 4 cm.

The sides of the triangle are 4 cm.