Triangle arm

There is an isosceles triangle with a circumference of 36 cm, and the height at the base is 12 cm long. Calculate the length of the arm of a given triangle.

Final Answer:

r =  13 cm

Step-by-step explanation:

$$\begin{gathered} o=36\text{cm} \\ h=12\text{cm} \\ o=2r+a \\ {h}^2=r^2-(a/2{)}^2 \\ 12^2=r^2-((36-2r)/2{)}^2 \\ 144=r^2-(18-r{)}^2 \\ 144=r^2-(18^2-2\cdot 18r+r^2) \\ -36r+468=0 \\ r=468/36=13\text{cm} \end{gathered}$$

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