The hypotenuse of the isosceles right triangle with an area of 8 cm² is 4√2 cm.
Here's how to find it:
- Isosceles Right Triangle Properties: An isosceles right triangle has two equal sides (legs) and a right angle. The ratio of its sides is 1:1:√2.
- Area Formula: The area of a triangle is calculated as (1/2) base height. In an isosceles right triangle, the base and height are equal to the length of its legs.
- Solving for the Leg: Since the area is 8 cm², we can set up the equation: (1/2) leg leg = 8 cm². Solving for the leg, we get leg = √16 cm = 4 cm.
- Finding the Hypotenuse: The hypotenuse is √2 times the length of the leg. Therefore, the hypotenuse is 4√2 cm.
In summary:
- Area of the triangle = 8 cm²
- Leg length = 4 cm
- Hypotenuse = 4√2 cm
