Question

In triunghiul AVC se cunosc AB =2 cm AC =4√3 cm si BC= 2√13 cm , stabiliti natura triunghiului ABC
Daca AD perpendicular pe BC , D apartine lui BC calculati  AD BD si DC

Answer 1

ΔABC

AB=2          =>AB²=4
AC=4√3     =>AC²=(4√3)²= 48
BC=2√13   =>BC²=(2√13)²= 52

4+48=52
AB²+AC²=BC²      =>ΔABC -dreptunghic, mas<A=90

fie [AD] _|_ [BC]
AD-h

AD=AB* AC/BC=  2  * 4√3/2√13=  4√3/√13=  4√39/13

ΔADB, mas<D=90

BD²= AB²-AD²=  2² - (4√39/13)²=  4 - 624/169=  (676-624)/169= 52/169

=>BD= 2√13/13

DC=BC-BD=  2√13 -2√13/13=  (26√13 -2√13)/13= 24√13/13