Certainly! Let's solve for the perimeter of an isosceles right triangle where each leg measures 5 cm.
1. Identify triangle properties:
- In an isosceles right triangle, the two legs are equal.
- Let's denote the length of each leg as [tex]\( a \)[/tex].
2. Given values:
- Each leg length [tex]\( a = 5 \)[/tex] cm.
3. Calculate the hypotenuse [tex]\( c \)[/tex]:
- According to the Pythagorean theorem:
[tex]\[
c = \sqrt{a^2 + a^2} = \sqrt{2a^2} = a\sqrt{2}
\][/tex]
- Substitute the given value [tex]\( a = 5 \)[/tex]:
[tex]\[
c = 5\sqrt{2} \approx 7.0710678118654755 \text{ cm}
\][/tex]
4. Calculate the perimeter [tex]\( P \)[/tex]:
- The perimeter of the triangle is the sum of the lengths of its three sides:
[tex]\[
P = a + a + c = 2a + c
\][/tex]
- Substitute [tex]\( a = 5 \)[/tex] and [tex]\( c = 5\sqrt{2} \)[/tex]:
[tex]\[
P = 2(5) + 5\sqrt{2} = 10 + 5\sqrt{2} \approx 17.071067811865476 \text{ cm}
\][/tex]
The perimeter of the isosceles right triangle is [tex]\( 10 + 5\sqrt{2} \)[/tex] cm.
So, the correct answer is:
C) [tex]\( 10 + 5\sqrt{2} \)[/tex] cm.
