Question

Sa se afle inaltimea unui triunghi echilateral cu Aria de 60√3 cm^2.

Answer 1

[tex]A_{\triangle~echilateral}=60 \sqrt{3}cm^2 \\ \frac{l^2 \sqrt{3} }{4}=60 \sqrt{3} \\ l^2 \sqrt{3}=60 \sqrt{3}*4|: \sqrt{3} \\ l^2=60*4 \\ 240|5*2 \\ ..24|2 \\ ..12|2~~~~~~~~\Longrightarrow l= \sqrt{5*3*2^3}=\underline{2 \sqrt{30}} \\ ....6|2 \\ ....3|3 \\ h_{\triangle~echilateral}= \frac{l \sqrt{3} }{2}= \frac{2 \sqrt{90} }{2}= \sqrt{90} \\ 90|2 \\ 45|5~~~~~~~~~~\Longrightarrow \boxed{h=3 \sqrt{10}} \\ ..9|3^2 [/tex]