Question

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Answer 1

Răspuns:

AB = 8 cm; AC = 12 cm

Explicație pas cu pas:

ABC triunghi dreptunghic; BC ipotenuza 4√3 cm; raportul catetelor este 2/3:

$\frac{AB}{AC} = \frac{2}{3} = > AB = \frac{2AC}{3}$

$AB²+AC²=BC² \\ ( \frac{2AC}{3})^{2} + AC² = (4 \sqrt{13})^{2} \\ \frac{4AC²}{9} + AC² = 13 \times 16 \\ \frac{13AC²}{9} = 13 \times 16 = > AC² = 9 \times 16 \\ = > AC = 12 \: cm$

$AB = \frac{2 \times 12}{3} = > AB = 8 \: cm$

Answer 2

$\it BC=4\sqrt{13} \Rightarrow BC^2=16\cdot13\ \ \ \ \ (1)\\ \\ \dfrac{AB}{AC}=\dfrac{2}{3} \Rightarrow \dfrac{AB^2}{AC^2}=\dfrac{4}{9} \Rightarrow \dfrac{AB^2+AC^2}{AC^2}=\dfrac{4+9}{9} \stackrel{TP}{\Longrightarrow}\dfrac{BC^2}{AC^2}=\dfrac{13}{9}\stackrel{(1)}{\Longrightarrow}\\ \\ \\ \Rightarrow \dfrac{16\cdot13}{AC^2}=\dfrac{13}{9} \Rightarrow \dfrac{16}{AC^2}=\dfrac{1}{9} \Rightarrow AC^2=16\cdot9=144=12^2 \Rightarrow AC=12\ cm$

$\it TP \Rightarrow AB^2=BC^2-AC^2=16\cdot13-16\cdot9=16\cdot4=64=8^2 \Rightarrow AB=8cm$