Question

Tam giác ABC vuông tại A,BC=12,AB/AC=2/3.Tính AB,AC

 

Answer 1

Ta có: \(\frac{AB}{AC}=\frac{2}{3}\Rightarrow AB=\frac{2}{3}AC\Rightarrow AB^2=\frac{4}{9}AC^2\)

Mặt khác: AB² + AC² = BC²

\(\Rightarrow\frac{4}{9}AC^2+AC^2=BC^2=12^2=144\)

\(\Rightarrow\frac{13}{9}AC^2=144\Rightarrow AC^2=\frac{1296}{13}\Rightarrow AC=\frac{36}{\sqrt{13}}\)

\(\Rightarrow AB=\frac{2}{3}AC=\frac{2}{3}.\frac{36}{\sqrt{13}}=\frac{24}{\sqrt{13}}\)

      Vậy \(AB=\frac{24}{\sqrt{13}};AC=\frac{36}{\sqrt{13}}\)