Base of an isosceles triangle

Calculate the size of the base of an isosceles triangle, the height is 5 cm and the length of the arm is 6.5 cm. What is the perimeter of this triangle?

Correct answer:

a =  8.3066 cm

Step-by-step explanation:

$$\begin{gathered} h=5\text{ cm } \\ r=6.5\text{ cm } \\ (a\mathrm{/}2{)}^2+h^2=r^2=6.5^2={\displaystyle \frac{169}{4}}=42.25 \\ a=2\cdot \sqrt{r^2-h^2}=2\cdot \sqrt{6.5^2-5^2}=\sqrt{69}=8.3066\text{ cm} \end{gathered}$$

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