Problema: Num canteiro quadrado, como o que se representa na figura, a Clara vai plantar os lírios no quadrado azul e os jarros no quadrado verde. Qual é a razão entre a área do quadrado com jarros e a área do quadrado com lírios? (image1)


Conteúdo referenciado:
[image1]
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Opções:
A) $\displaystyle\frac{2}{3}$
B) $\displaystyle\frac{\sqrt{2}}{\sqrt{3}}$
C) $\displaystyle\frac{8}{9}$
D) $1$
E) $\displaystyle\frac{9}{8}$

Resolução: [(c)] Os triângulos rectângulos $[DGF]$ e $[FEB]$ são isósceles e congruentes, logo $\overline{AE}= \frac{1}{2} \: \overline{AB}$. De modo análogo, os triângulos rectângulos $[KHD]$ e $[JIB]$ também são isósceles e congruentes, logo $\overline{HI}= \frac{1}{3} \overline{DB}= \frac{\sqrt{2}}{3} \overline{AB}$. Assim, a razão entre as áreas do quadrado com jarros e do quadrado com lírios é $\frac{\frac{2}{9} \overline{AB}^2}{\frac{1}{4} \overline{AB}^2}= \frac{8}{9}$. Opção correcta: C). (image2)


Conteúdo referenciado:
[image2]
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Resposta correta: C