Sure, let's solve this step-by-step.
1. Identify the Known Values:
Each of the equal sides of the isosceles right triangle is 10 cm.
2. Use the Pythagorean Theorem to Find the Hypotenuse:
In an isosceles right triangle, the two equal sides form the legs of the triangle. According to the Pythagorean theorem, the hypotenuse ([tex]\(c\)[/tex]) can be found using the formula:
[tex]\(c = \sqrt{a^2 + b^2}\)[/tex]
Since [tex]\(a = b\)[/tex], this simplifies to:
[tex]\(c = \sqrt{2a^2}\)[/tex]
With [tex]\(a = 10\)[/tex], we get:
[tex]\(c = \sqrt{2 \times (10)^2} = \sqrt{200} ≈ 14.142135623730951\)[/tex] cm
3. Calculate the Perimeter:
The perimeter of the triangle is the sum of all three sides:
Perimeter = [tex]\(a + b + c = 10 + 10 + 14.142135623730951 = 34.14213562373095\)[/tex] cm
4. Find the Semi-Perimeter:
The semi-perimeter is half of the perimeter:
Semi-perimeter = [tex]\(\frac{Perimeter}{2} = \frac{34.14213562373095}{2} ≈ 17.071067811865476\)[/tex] cm
Therefore, the semi-perimeter of the isosceles right triangle is approximately [tex]\(17.071067811865476\)[/tex] cm.
