The hypotenuse of a 45 -45 -90° triangle measures 4 cm period what is the length of one leg of the triangle?

The rule for 45-45-90 triangle is 1x-1x-sqrt2 x
So the other leg would be 4

one leg of the triangle = 2√2 cm

Explanation:
We are given that the triangle is 45°-45°-90°
This means that it is an isosceles triangle where the two legs are equal

Assume that each leg is x cm

Now, since it is a right-angled triangle, we can apply the Pythagorean theorem to get the length of each leg as follows:
(hypotenuse)² = (first leg)² + (second leg)²
(4)² = (x)² + (x)²
16 = 2x²
x² = 8
either x = √8 = 2√2 cm > accepted
or x = -√8 = -2√2 cm > rejected as length cannot be negative

Based on the above, each leg of the triangle given would be 2√2 cm

Hope this helps :)