Question

A figura a seguir mostra um retangulo ABCD e a diagonal AC. Sabendo que tg alfa=1/4, determine a medida da área desse triângulo.

Answer 1

$\displaystyle \text{tg }\alpha = \frac{1}{4} \to \text{tg }\alpha = \frac{\text{CD}}{\text{AD}} \\\\ \therefore \\\\ \frac{1}{4} = \frac{\text x}{\text x+15} \to 4\text x=\text x+15 \\\\ 3\text x=15 \to \boxed{\text x = 5}$

Área :

$\displaystyle \text S_{\text{ABCD}}= \text{AC.CD} \\\\ \text S_{\text{ABCD}}= \text{(5+15)5 } \\\\ \text S_{\text{ABCD}}= \text{20.5} \\\\ \underline{\text{Portanto a {\'a}rea do ret{\^a}ngulo vale}}:\\\\ \huge\boxed{\text S_{\text{ABCD}}=100 \ }$