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In triunghiul ABC cu m=(<A)=90°, [AD] inaltime, BC=10√2cm si BD/DC = 3/2. Aflati AD.

Răspuns :

BD/DC=3/2 ⇒ (BD+DC)/DC=5/2 ⇒ DC=2BC/5=4√2 cm; BD=BC-DC=6√2 cm;
teorema inaltimii in ΔABC: AD²=BD·DC=48 cm ⇒ AD=√48=4√3 cm.
BD/DC=3/2 deci BD/BC=3/5. BD/10radical2 =3/5 BD=6radical2 DC=4radical2 Din teorema inaltimii AD^2=6rad2*4rad2=48 Deci AD=4radical din 3

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