Question

Urgent! Dau coroanaaa!
Fie triunghiul MNP.
$mn =mp = \sqrt{3} \\ \tan(n) = \sqrt{3}$
Perimetru=?
Aria =? ​

Answer 1

Răspuns:

$P_{\triangle MNP}=3\sqrt{3};\\A_{\triangle MNP}=\frac{3\sqrt{3}}{4}.$

Explicație pas cu pas:

$\tan{\sphericalangle MNP}=\sqrt{3}\Rightarrow m\sphericalangle MNP=60\°\\\substack{MN\equiv MP}\Rightarrow \triangle MNP \text{ isoscel}.\\\\\substack{\triangle MNP\text{ isoscel}\\m\sphericalangle MNP=60\°}\}\Rightarrow\triangle MNP\text{ echilateral}$

Deoarece $\triangle MNP$ echi., putem folosi formulele acestui tip de triunghi:

$P_{\triangle\text{echi.}}}=\text{latura}\cdot3$;

$A_{\triangle\text{echi.}}=\frac{\text{latura}^2\sqrt{3}}{4}$.

Deci:

$P_{\triangle MNP}=3\cdot MN\\\Rightarrow P_{\triangle MNP}=3\sqrt{3}.$

$A_{\triangle MNP}=\frac{MN^2\sqrt{3}}{4}\\=\frac{\sqrt{3}^2\sqrt3}{4}\\=\frac{3\sqrt{3}}{4}$