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 (\(\(c\)\)) can be found using the formula:
\(\(c = \sqrt{a^2 + b^2}\)\)
Since \(\(a = b\)\), this simplifies to:
\(\(c = \sqrt{2a^2}\)\)
With \(\(a = 10\)\), we get:
\(\(c = \sqrt{2 \times (10)^2} = \sqrt{200} ≈ 14.142135623730951\)\) cm
3. Calculate the Perimeter:
The perimeter of the triangle is the sum of all three sides:
Perimeter = \(\(a + b + c = 10 + 10 + 14.142135623730951 = 34.14213562373095\)\) cm
4. Find the Semi-Perimeter:
The semi-perimeter is half of the perimeter:
Semi-perimeter = \(\(\frac{Perimeter}{2} = \frac{34.14213562373095}{2} ≈ 17.071067811865476\)\) cm
Therefore, the semi-perimeter of the isosceles right triangle is approximately \(\(17.071067811865476\)\) cm.
