The Area of a Right Isosceles Triangle

To find the perimeter of a right isosceles triangle, we first need to understand its properties and formulas associated with it.

Properties of a Right Isosceles Triangle:
- A right isosceles triangle has two sides of equal length, and the angle between those sides is 90 degrees.
- The length of each of the two equal sides is denoted by 'a'.
- The length of the hypotenuse is denoted by 'c'.

Formulas:
- Area of a triangle = (1/2) * base * height
- For a right isosceles triangle, the base and height are equal. Therefore, the formula for the area simplifies to: Area = (1/2) * a * a = (a^2)/2

Given:
Area of the triangle = 100 cm²

Finding the Length of the Sides:
Using the formula for the area of a right isosceles triangle, we can find the length of each side.
Area = (a^2)/2
100 = (a^2)/2
Multiplying both sides by 2: 200 = a^2
Taking the square root of both sides: √200 = a
Simplifying: √(100 * 2) = a
√(100 * 2) = a
√(100) * √(2) = a
10√2 = a

Finding the Perimeter:
The perimeter of a triangle is the sum of the lengths of its sides.
In a right isosceles triangle, there are two sides of length 'a' and one hypotenuse of length 'c'.

Perimeter = a + a + c
Since the triangle is isosceles, the hypotenuse is equal to one of the sides.
Perimeter = 2a + a
Perimeter = 3a

Substituting the Value of 'a':
Perimeter = 3 * 10√2
Perimeter = 30√2

Hence, the perimeter of the right isosceles triangle with an area of 100 cm² is 30√2 cm.