Question

In triunghiul ABC,dreptunghic in A,se stie ca BC=4radical13 cm si AB/AC=2/3
Determinati lungimile catetelor.
Pleaseee,dau coronita!!! Imi trb pt maine,va roog!!

Answer 1

$AB^2+AC^2=BC^2\Rightarrow AB^2+AC^2=16\cdot13$

$\dfrac{AB}{AC}=\dfrac23\Rightarrow \dfrac{AB^2}{AC^2}=\dfrac49\Rightarrow \dfrac{AB^2+AC^2 }{AC^2}=\dfrac{4+9}{9}\Rightarrow \dfrac{16\cdot13}{AC^2}=\dfrac{13}{9}\Rightarrow$

$\Rightarrow AC^2=9\cdot16\Rightarrow AC=12\ cm$

$\dfrac{AB}{12}=\dfrac23\Rightarrow AB=8\ cm.$