Question

In triunghiul ABC dreptunghic, masura unghiului A=90 grade, AD perpendicular pe BC, D apartine lui BC BD/CD=9/16, iar Aria este 2400 cm. Aflati:a) lungimea catetelor si a ipotenuzei b) lungimea inaltimii AD

Answer 1

Notam BD=9k    si DC=16k       astfel incat BD/CD=9/16
BD+DC=9k+16k=25k
teorema catetei
AB=√BD×BC=√9k×25k=15k
AC=√DC×BC=√16k×25k=20k
A=2400 cm
A=AB×AC/2
2400=15k×20k/2
300k²=4800
k²=4800:300=16  ⇒ k=√16=4
AB=15k=15×4=60 cm
AC=20k=20×4=80 cm
BC=25k=25×4=100 cm
BD=9k=9×4=36 cm
DC=16k=16×4=64 cm
teorema inaltimii
AD=√BD×DC=√36×64=6×8=48 cm