Answer:
ans = 12 cm
Given information:
The triangle is an isosceles right triangle.
The area of the triangle is 36√3 cm².
Step 1: Find the base and height of the triangle.
In an isosceles right triangle, the base and height are equal.
Let's call the base and height 'b'.
Area of a triangle = (1/2) × base × height
36√3 cm² = (1/2) × b × b
36√3 cm² = (1/2) × b²
b² = 72√3 cm²
b = √(72√3) cm
b = 6√3 cm
Step 2: Find the length of the hypotenuse.
In a right triangle, the hypotenuse is related to the base and height (legs) by the Pythagorean theorem.
Hypotenuse² = base² + height²
Hypotenuse² = (6√3)² + (6√3)²
Hypotenuse² = 72(2)
Hypotenuse² = 144
Hypotenuse = √144
Hypotenuse = 12 cm
Therefore, the length of the hypotenuse of the isosceles right triangle with an area of 36√3 cm² is 12 cm.