Question

VA ROG REPEDE : Fie triunghiul ABC,m(A)=90grade.AD perpendicular BC,D apartine BC,AB=12cm si BC=13cm. a)Calculati lungimea catetei AC. b)Aflati lungimea inaltimii AD. c)Calculati aria triunghiului ABC.

Answer 1

a)
AB²+AC²=BC²(t.Pit.)
AC²=BC²-AB²
AC²=(13-12)(13+12)
AC²=25 =>AC=5cm

b)
T.cat.AB²=BDxBC
144=BDx13 =>BD=144/13
T.cat.AC²=CDxBC 
25=CDx13 =>CD=25/13
T.inaltimii AD²=BDxCD
AD²=144/13x25/13
AD²=(144x25)/(13x13)
AD=(12x5)/13
AD=60/13

c)
Aria=semiprod.catetelor=12x5/2=30cm²