The area of an isosceles right triangle is S. What is the hypotenuse of this triangle?

Let a right-angled isosceles triangle ABC be given with the base AB, which is the hypotenuse. The area of ​​a right-angled triangle can be found as half of the product of the legs, that is, S (Δ ABC) = (AC ∙ BC): 2 = AC²: 2, since AC = BC. From the condition of the problem it is known that the area of ​​an isosceles right-angled triangle is S, then we express the length of the leg AC²: 2 = S; AC² = 2 ∙ S. Let us find the hypotenuse of this triangle according to the Pythagorean theorem: AB² = AC² + BC²; AB² = 2 ∙ AC²; AB² = 2 ∙ 2 ∙ S; AB² = 4 ∙ S; AB = 2 ∙ S ^ (½).
Answer: The hypotenuse of an isosceles right-angled triangle is 2 ∙ S ^ (½).