Question

Utilizando a regra do teorema de tales no triângulo, determine os valores de X;

Answer 1

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$\tt a)~\sf \triangle ADC\sim\triangle ABE\\\sf\dfrac{2x+6}{7}=\dfrac{x+6}{6}\\\sf 12x+36=7x+42\\\sf 12x-7x=42-36\\\sf 5x=6\\\sf x=\dfrac{6}{5}\checkmark$

$\tt b)~\sf\triangle ABC\sim\triangle ADE\\\sf \dfrac{13}{8}=\dfrac{x+8}{x}\\\sf 13x=8x+64\\\sf 13x-8x=64\\\sf 5x=64\\\sf x=\dfrac{64}{5}\checkmark$