Question

Answer 1

\(\dfrac{AB}{AC}=\dfrac{3}{4}\Leftrightarrow AB=\dfrac{3}{4}AC\)

Áp dụng HTL tam giác

\(\dfrac{1}{AH^2}=\dfrac{1}{AB^2}+\dfrac{1}{AC^2}\Leftrightarrow\dfrac{1}{12^2}=\dfrac{1}{\left(\dfrac{3}{4}AC\right)^2}+\dfrac{1}{AC^2}\\ \Leftrightarrow\dfrac{1}{144}=\dfrac{16}{9AC^2}+\dfrac{1}{AC^2}\Leftrightarrow\dfrac{1}{144}=\dfrac{25}{9AC^2}\\ \Leftrightarrow9AC^2=3600\Leftrightarrow AC^2=400\\ \Leftrightarrow AC=20\left(cm\right)\Leftrightarrow AB=\dfrac{3}{4}\cdot20=15\left(cm\right)\\ \Leftrightarrow S_{ABC}=\dfrac{1}{2}AB\cdot AC=\dfrac{1}{2}\cdot15\cdot20=150\left(cm^2\right)\)