Question

abc ab =3 cm bc =5 cm qc =4 cm be bis a unghiului b ae=?​

Answer 1

ΔABC dr in A

Reciproca teoremei lui Pitagora

5²=3²+4²

25=9+16

25=25

Teorema bisectoarei

$\frac{AB}{AE} =\frac{BC}{EC} \\\\\frac{3}{AE} =\frac{5}{EC} =k\\\\AE=\frac{k}{3} \\\\EC=\frac{k}{5}$

$AE+EC=AC=4$

$\frac{k}{3}+\frac{k}{5}=4$

5k+3k=60

8k=60

$k=\frac{15}{2} \\\\AE=\frac{15}{2}\times \frac{1}{3} =2,5$