How to find the leg of an isosceles triangle, knowing the hypotenuse?

In a right-angled triangle, according to the Pythagorean theorem, the square of the hypotenuse is equal to the sum of the squares of its legs. If we are given an isosceles right-angled triangle, then the square of the hypotenuse will be equal to the square of the legs multiplied by two. Let’s introduce the notation: take the hypotenuse for “a”, leg for “b”. Let’s write out, using “a” and “b” the Pythagorean theorem, and determine the value of the leg:

a ^ 2 = b ^ 2 + b ^ 2

a ^ 2 = 2b ^ 2

b ^ 2 = a ^ 2/2

b = sqrt (a ^ 2/2)

Thus, the leg is equal to the square root of the hypotenuse squared, divided by two.