Question

Triunghiul ABC ,m(A)=90,AB/AC =3/4 ,BC=15 cm .perimetrul triunghiului ABC este...

Answer 1

AB/AC= 3/4 rezulta ca AB are 3 parti, iar AC are 4 parti. Fiind triunghi dreptunghic, faci pitagora si afli cat este o parte.

Answer 2

$\it \dfrac{AB}{AC} = \dfrac{3}{4} \Rightarrow \dfrac{AB^2}{AC^2} = \dfrac{9}{16} \Rightarrow \dfrac{AB^2}{AC^2+AB^2} =\dfrac{9}{9+16} \ \ \stackrel{T.Pitagora}{\Longrightarrow}\ \dfrac{AB^2}{BC^2} = \dfrac{9}{25}\Rightarrow \\ \\ \\ \Rightarrow \dfrac{AB^2}{15^2} = \dfrac{3^2}{5^2}\Rightarrow AB^2=\dfrac{15^2\cdot3^2}{5^2} \Rightarrow AB^2=\left(\dfrac{15\cdot3}{5}\right)^2 \Rightarrow AB = \dfrac{15\cdot3}{5} \Rightarrow \\ \\ \\ \Rightarrow AB = 3\cdot3 \Rightarrow AB = 9cm\ \ \ \ \ (*)$

$\it \dfrac{AB}{AC} = \dfrac{3}{4} \stackrel{(*)}{\Longrightarrow} \dfrac{9}{AC}=\dfrac{3}{4} \Rightarrow AC = \dfrac{9\cdot4}{3} \Rightarrow AC = 12\ cm \\ \\ \\ \mathcal{P} = AB+AC+BC =9+12+15 =36\ cm$