Find the length of the hypotenuse of an isosceles right-angled triangle with an area of 100cm².

From the condition we know that we are given a right-angled isosceles triangle and its known area is 100 cm ^ 2. We need to find the length of the hypotenuse.

We start by recalling the formula for finding the area of a right-angled triangle, through the lengths of the legs:

S = 1/2 * a * b;

The lengths of the legs are the same, since the triangle is isosceles. Let’s denote by x cm the length of the legs and write the equation:

100 = 1/2 * x ^ 2;

x ^ 2 = 200;

x = 10√2 cm legs.

Let’s apply the Pythagorean theorem:

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

c = √ (10√2) ^ 2 + (10√2) ^ 2 = √400 = 20 cm.