To determine the perimeter of an isosceles triangle with a given height and base, let's follow the step-by-step method.
1. Identify the given information:
- The height of the triangle [tex]\( h = 12 \)[/tex] cm
- The base of the triangle [tex]\( b = 10 \)[/tex] cm
2. Calculate half the base:
The base of the isosceles triangle is divided into two equal parts by the height. Each part is:
[tex]\[
\text{half_base} = \frac{b}{2} = \frac{10}{2} = 5 \text{ cm}
\][/tex]
3. Calculate the length of the two equal sides:
Using the Pythagorean theorem for the right triangle formed by the height, half the base, and one of the equal sides:
[tex]\[
\text{equal_side} = \sqrt{h^2 + \text{half_base}^2}
\][/tex]
Substituting the given values:
[tex]\[
\text{equal_side} = \sqrt{12^2 + 5^2} = \sqrt{144 + 25} = \sqrt{169} = 13 \text{ cm}
\][/tex]
4. Calculate the perimeter of the isosceles triangle:
The perimeter [tex]\( P \)[/tex] is the sum of all three sides, i.e., the base and the two equal sides:
[tex]\[
P = b + 2 \times \text{equal_side}
\][/tex]
Substituting the known values:
[tex]\[
P = 10 + 2 \times 13 = 10 + 26 = 36 \text{ cm}
\][/tex]
Hence, the perimeter of the isosceles triangle is [tex]\( 36 \)[/tex] cm.
So, the correct answer is:
OB) 36 cm.
