Question

O perímetro do triângulo vale:

a) 10,4 cm
b) 34 cm
c) 11 cm
d) 34,4 cm ​

Answer 1

$\Large\boxed{\begin{array}{l}\sf\triangle ABC\sim \triangle ADE\\\sf\dfrac{6,4+2x}{6,4}=\dfrac{x^2+4x+1}{4x}\\\\\sf 8x^2+25,6x=6,4x^2+25,6x+6,4\\\sf 8x^2-6,4x^2+\diagup\!\!\!\!\!\!25,6x-\diagup\!\!\!\!\!25,6x=6,4\\\sf 1,6x^2=6,4\\\sf x^2=\dfrac{6,4}{1,6}\\\\\sf x^2=4\\\sf x=\sqrt{4}\\\sf x=2~cm\\\sf AB=6,4+2\cdot2=10,4\,cm\\\sf BC=3\cdot2+5=11\,cm\\\sf AC=4\cdot2+2^2+1=13\,cm\\\sf 2p\longrightarrow per\acute imetro\\\sf 2p=AB+BC+AC\\\sf 2p=10,4+11+13\\\sf 2p=34,4\,cm\end{array}}$

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