A right-angled isosceles triangle has an area of 50 square units. Its…

Define the properties:
In a right-angled isosceles triangle, the two legs are of equal length. Let the length of each leg be a.

Use the Area formula:
The area of a right triangle is (1/2) * base * height. Since the legs are equal (base = height = a):
Area = (1/2) * a * a = (1/2) * a²
Given the area is 50:
50 = (1/2) * a²
100 = a²
a = 10 units

Calculate the Hypotenuse:
According to the Pythagorean theorem, for a triangle with legs a, the hypotenuse h is:
h = sqrt(a² + a²) = sqrt(2a²) = a * sqrt(2)
Substituting a = 10:
h = 10 * sqrt(2)