Question

Calcule a área de um triangulo retângulo cuja a hipotenusa mede 2√¯41 m e, um dos catetos 8 m.

Answer 1

$\textrm{Calculando a medida do outro cateto:}\\\\ \mathrm{cat_1^2+cat_2^2=hip^2\ \to\ a^2+b^2=c^2}\\\\ \mathrm{a^2+8^2=(2\sqrt{41})^2\ \to\ a^2+64=4.41}\\\\ \mathrm{a^2=164-64\ \to\ a^2=100}\\\\ \mathrm{a=\sqrt{100}\ \to\ a=10\ m}\\\\ \mathrm{Calculando\ a\ \'area:}\\\\ \mathrm{S=\dfrac{cat_1.cat_2}{2}\ \to\ S=\dfrac{a.b}{2}}\\\\ \mathrm{S=\dfrac{8.10}{2}=\dfrac{80}{2}\ \to\ \boxed{\mathbf{S=40\ m^2}}}$