Calculate 35083

Draw an isosceles triangle ABC with a base 7 cm long and shoulders 5.5 cm long. Assemble all the heights, measure them, and calculate their sum.

Correct answer:

s =  15.0421 cm

Step-by-step explanation:

$$\begin{gathered} a=7\text{cm} \\ r=5.5\text{cm} \\ {v}_1=\sqrt{r^2-(a/2{)}^2}=\sqrt{5.5^2-(7/2{)}^2}=3\sqrt{2}\text{cm}\doteq 4.2426\text{cm} \\ S=\frac{a\cdot v_1}{2}=\frac{7\cdot 4.2426}{2}\doteq 14.8492{\text{cm}}^2 \\ S=\frac{r\cdot v_2}{2} \\ {v}_2=2\cdot S/r=2\cdot 14.8492/5.5\doteq 5.3997\text{cm} \\ {v}_3=v_2=5.3997\doteq 5.3997\text{cm} \\ s=v_1+v_2+v_3=4.2426+5.3997+5.3997=15.0421\text{cm} \end{gathered}$$

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