Find the hypotenuse of an isosceles right-angled triangle if its area is 32 cm².

The area of a right-angled triangle is half the product of the lengths of its legs, and in the case of an isosceles right-angled triangle, half the square of the length of the legs:

S = 0.5 * a * a = 0.5 * a ^ 2.

From here we can find the length of the leg: a ^ 2 = 2 * S;

a = √ (2 * S) = √ (2 * 32) = √64 = 8 cm.

The square of the hypotenuse is equal to the sum of the squares of the legs: a ^ 2 + a ^ 2 = c ^ 2, which means

c = √ (a ^ 2 + a ^ 2) = √ (2 * a ^ 2) = a√2 = 8√2 ≈ 11.3 cm.