Question

Me ajudem por favor!!!

Answer 1

Resposta:

$\overline{AB}=40\\\\\overline{AC}=80$

Explicação passo a passo:

Note que pelo caso $AA$ os triângulos $\triangle ADE$ e $\triangle ABC$ são semelhantes.

Disso:

$\frac{\overline{AD}}{\overline{AB}}=\frac{\overline{AE}}{\overline{AC}}$

Substituindo, teremos:

$\frac{25}{25+(x-5)}=\frac{x+30}{(x+30)+(x+10)}\\\\\frac{25}{25+x-5}=\frac{x+30}{x+30+x+10}\\\\\frac{25}{x+20}=\frac{x+30}{2x+40}\\\\(x+20)\cdot(x+30)=25\cdot(2x+40)\\\\x^2+30x+20x+600=50x+1000\\\\x^2+50x+600=50x+1000\\\\x^2+600=1000\\\\x^2=400\\\\x=\pm20$

Como $x > 5$, logo $x=20$.

Portanto:

$\overline{AB}=25+20-5=40\\\\\overline{AC}=20+30+20+10=80$