Question

Na figura abaixo o triângulo ABC~EAD,AD=14 cm, ED= 12 cm,BC= 15 cm e EB= 4 cm. Determine as medidas de AC, AE e AB?

Answer 1

Boa tarde

$a)\quad \dfrac{ED}{BC}= \dfrac{AD}{AC} \Rightarrow \dfrac{12}{15}= \dfrac{14}{AC} \\ \\ \\ AC= \dfrac{15*14}{12} = \dfrac{5*14}{4} \Rightarrow \boxed{AC=17,5}$

$b) \quad \dfrac{AD}{AC}= \dfrac{AE}{AB} \Rightarrow \dfrac{14}{17,5}= \dfrac{AE}{AE+4} \\ \\ \\ 17,5AE=14*(AE+4)\Rightarrow 17,5AE=14*AE+56 \\ \\ \\ 3,5*AE =56 \Rightarrow AE= \dfrac{56}{3,5}\Rightarrow \boxed{AE=16} \\ \\ c)\quad AB= 16+4 \Rightarrow \boxed{AB=20}$