Question

\(\Delta ABC\) vuông tại A. Đường cao AH = 24cm. AB:AC = 3:4. BH, CH = ?

Answer 1

Ta có: \(\dfrac{AB}{AC}=\dfrac{3}{4}\)

\(\Leftrightarrow\dfrac{HB}{HC}=\dfrac{9}{16}\)

\(\Leftrightarrow HB=\dfrac{9}{16}\cdot HC\)

Ta có: \(AH^2=HB\cdot HC\)

\(\Leftrightarrow HC^2\cdot\dfrac{9}{16}=24^2\)

\(\Leftrightarrow HC=32\left(cm\right)\)

hay HB=18(cm)