Question

preciso saber qual a resposta dessas duas questões ​

Answer 1

a) pelo teorema de Tales:

$\frac{4}{12} = \frac{b}{c} = k \\ \frac{1}{3} = \frac{b}{c} = k \\ \frac{c}{3} = \frac{b}{1} = k$

$c = 3k \\ b = k \\ b + c = 24 \\ 3k + k = 24 \\ 4k = 24$

$k = \frac{24}{4} = 6$

$c= 3k = 3.6 = 18$

$b = k = 6$

Ainda pelo teorema de Tales:

$\frac{6}{4} = \frac{a}{b} \\ \frac{3}{2} = \frac{a}{6} \\ 2a = 18 \\ a = \frac{18}{2} = 9$

b) pelo teorema de Tales:

$\frac{a - 11}{11} = \frac{8}{6} \\ \frac{a - 11}{11} = \frac{4}{3}$

$3a - 33 = 44 \\ 3a = 77 \\ a = \frac{77}{3}$

$\frac{b}{a - 11} = \frac{8}{8} \\ \frac{b}{a - 11} = 1 \\ b =a - 11 \\ b = \frac{77}{3} - 11$

$b = \frac{77 - 33}{ 3} = \frac{44}{3}$

$\frac{c}{b} = \frac{12}{8} \\ \frac{c}{b} = \frac{3}{2} \\ c = \frac{3}{2} b$

$c = \frac{3}{2} \frac{44}{3} = 22$