Question

Calcular a área de um triângulo equilátero cujo perímetro é 30 m.

Answer 1

$\mathrm{Como\ o\ \bigtriangleup\ em\ quest\~ao\ \'e\ equil\'atero,}\\ \textrm{seu per\'imetro \'e igual a}\ \mathbf{3\times lado:}\\\\ \mathrm{P=3l\ \to\ 30=3l\ \to\ l=\dfrac{30}{3}\ \to\ \boxed{\mathrm{l=10\ m}}}\\\\ \mathrm{A\ \'area\ de\ um\ \bigtriangleup\ equil\'atero\ \'e\ dada}\\ \mathrm{por\ \mathbf{l^2\sqrt{3}/4:}}\\\\ \mathrm{S=\dfrac{l^2\sqrt{3}}{4}=\dfrac{10^2\sqrt{3}}{4}=\dfrac{100\sqrt{3}}{4}\ \to\ \boxed{\mathbf{S=25\sqrt{3}\ m^2}}}$