Question

As figuras abaixo nos mostram pares de triangulos semelhantes.calcule x e y em cada uma delas

Answer 1

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$\tt a)~\sf\dfrac{x}{18}=\dfrac{12}{9}\\\sf\dfrac{x}{18\div9}=\dfrac{12}{9\div9}\\\sf \dfrac{x}{2}=12\\\sf x=2\cdot12\\\huge\boxed{\boxed{\boxed{\boxed{\sf x=24}}}}\\\sf\dfrac{18}{y}=\dfrac{12}{9}\\\sf\dfrac{18\div6}{y}=\dfrac{12\div6}{9}\\\sf\dfrac{3}{y}=\dfrac{2}{9}\\\sf 2\cdot y=3\cdot9\\\sf 2y=27\\\huge\boxed{\boxed{\boxed{\boxed{\sf y=\dfrac{27}{2}}}}}$

$\tt b)~\sf\dfrac{x}{10}=\dfrac{3}{9}\\\sf\dfrac{x}{10}=\dfrac{3\div3}{9\div3}\\\sf\dfrac{x}{10}=\dfrac{1}{3}\\\huge\boxed{\boxed{\boxed{\boxed{\sf x=\dfrac{10}{3}}}}}\\\sf\dfrac{y}{6}=\dfrac{3}{9}\\\sf\dfrac{y}{6\div3}=\dfrac{3}{9\div3}\\\sf\dfrac{y}{2}=\dfrac{\diagup\!\!\!3}{\diagup\!\!\!3}\\\sf\dfrac{y}{2}=1\\\sf y=2\cdot1\\\huge\boxed{\boxed{\boxed{\boxed{\sf y=2}}}}$