Find the area of a right-angled isosceles triangle with a hypotenuse equal to 10 cm.

Let x cm be the length of the side of a given triangle.

The triangle is isosceles, therefore its second lateral side is equal to x cm.

Since the triangle is rectangular, its sides are legs.

According to the Pythagorean theorem, the sum of the squares of the legs is equal to the square of the hypotenuse of a right-angled triangle, so we can write:

x ^ 2 + x ^ 2 = 10 ^ 2;

2x ^ 2 = 100;

x ^ 2 = 50;

x = √50 = 5√2.

5√2 cm – leg length.

The area of a right-angled triangle (S) is equal to half the product of its legs:

S = 1/2 * 5√2 * 5√2 = 25 cm ^ 2.

Answer: 25 cm ^ 2.