Question

Va rog daca nu stiti nu raspundeti
Doar ex 41

Answer 1

    
[tex] \text{Am atasat desenele notate, iar rezolvarea o voi face aici. } \\ \text{Suntem la capitolul "ASEMANAREA TRIUNGHIURILOR"} \\ \\ a) \displaystyle\\ In~ disenul~~a)~~avem: \\ \Delta ABC ~~si ~~\Delta CDE ~~avem: \\ \widehat{ABC}=\widehat{CDE}=90^o \\ \widehat{ACB}=\widehat{CED} \\ \Longrightarrow ~~~\text{suntem in cazul UU de asemanare } \\ \Longrightarrow ~~~\Delta ABC ~\sim~\Delta CDE \\ \text{Scriem rapoartele de asemanare: } \\ \\ \frac{AB}{CD}= \frac{BC}{DE} [/tex]

[tex]\displaystyle \\ \frac{AB}{CD}= \frac{BC}{DE} \\ \\ \frac{x-1,4}{10}= \frac{12}{x+5,6} \\ \\ (x-1,4)(x+5,6)=10 \cdot 12 \\ x^2 -1,4x + 5,6x- 1,4\cdot 5,6 = 120 \\ x^2 -4,2x- 7,84 - 120=0 \\ x^2 -4,2x - 127,84=0 \\ \\ x_{12}= \frac{-b \pm \sqrt{b^2 -4ac} }{2a} =\frac{7,84 \pm \sqrt{17,64 +511,36} }{2} = \\ \\ \frac{7,84 \pm \sqrt{529} }{2} =\frac{7,84 \pm 23}{2} \\ \\ x_1 = \frac{7,84 + 23}{2} = \frac{30,84}{2} = \boxed{15,42} [/tex]

[tex]\displaystyle \\ \\ x_2 = \frac{7,84 - 23}{2} =\frac{-15,16}{2}= -7,58 \\ \\ \text{Aceasta solutie va fi eliminata deoarece laturile ar ar fi negative } [/tex]



[tex]b) \displaystyle\\ In~ disenul~~b)~~avem: \\ \Delta ABE ~~si ~~\Delta CBD ~~in~care~ avem: \\ \widehat{ABE}= \widehat{CBD}~~~fiind~opuse~la~varf. \\ \widehat{BAE}=\widehat{BCD} \\ \Longrightarrow ~~~\text{suntem in cazul UU de asemanare } \\ \Longrightarrow ~~~\Delta ABE ~\sim~\Delta CBD \\ \text{Scriem rapoartele de asemanare: } \\ \\ \frac{AB}{CB}= \frac{BE}{BD} \\ \\ \frac{18}{12,6}= \frac{x+2}{x-1} \\ \\ 18(x-1)= 12,6(x+2) [/tex]

[tex]\displaystyle \\ 18x -12,6x = 25,2+18 \\ 5,4x=43,2 \\ \\ x = \frac{43,2}{5,4}=\boxed{8} [/tex]