-Xét △ABC có: ED//AC; FD//AB.
\(\Rightarrow\)△EBD∼△ABC ; FDC∼△ABC.
\(\Rightarrow\dfrac{S_{EBD}}{S_{ABC}}=\left(\dfrac{BD}{BC}\right)^2\) ; \(\dfrac{S_{FDC}}{S_{ABC}}=\left(\dfrac{DC}{BC}\right)^2\)
\(\Rightarrow\sqrt{\dfrac{S_{EBD}}{S_{ABC}}}=\dfrac{BD}{BC};\sqrt{\dfrac{S_{FDC}}{S_{ABC}}}=\dfrac{DC}{BC}\)
\(\Rightarrow\sqrt{\dfrac{a^2}{S_{ABC}}}=\dfrac{BD}{BC};\sqrt{\dfrac{b^2}{S_{ABC}}}=\dfrac{DC}{BC}\)
\(\Rightarrow\dfrac{\sqrt{a^2}}{\sqrt{S_{ABC}}}=\dfrac{BD}{BC};\dfrac{\sqrt{b^2}}{\sqrt{S_{ABC}}}=\dfrac{DC}{BC}\)
\(\Rightarrow\dfrac{a}{\sqrt{S_{ABC}}}=\dfrac{BD}{BC};\dfrac{b}{\sqrt{S_{ABC}}}=\dfrac{DC}{BC}\)
\(\Rightarrow\dfrac{a+b}{\sqrt{S_{ABC}}}=\dfrac{BD}{BC}+\dfrac{DC}{BC}=\dfrac{BC}{BC}=1\)
\(\Rightarrow\sqrt{S_{ABC}}=a+b\)
\(\Rightarrow S_{ABC}=\sqrt{a+b}\)
