Question

22. Un triunghi echilateral are înălțimea de 3 cm. Găsiţi aria triunghiului.​

Answer 1

$\it Fie\ h- \^{i}n\breve al\c{\it t}imea,\ \ \ \ell-\ latura \ triunghiului.$

$\it h=\dfrac{\ell\sqrt3}{2} \Rightarrow 3=\dfrac{\ell\sqrt3}{2}\Rightarrow \sqrt3\cdot\sqrt3 =\dfrac{\ell\sqrt3}{2}|_{:\sqrt3}\Rightarrow \sqrt3=\dfrac{\ell}{2} \Rightarrow \ell=2\sqrt3$

$\it \mathcal{A}=\dfrac{\ell^2\sqrt3}{4}=\dfrac{(2\sqrt3)^2\sqrt3}{4}=\dfrac{\not4\cdot3\sqrt3}{\not4}=3\sqrt3\ cm^2$