Question

Triunghiul dreptungic ABC mA=90° AD perpendicular BC , D € BC are AB/AC=3/4 si aria egala cu 216 cm ^2 Aflati: a) perimetrul triunghiului b)lungimea înălțimii AD c) lungimile segmentelor BD si CD

Answer 1

Salut,

AB/AC=3/4⇒AB=3/4AC;
A=AB*AC/2;
216=3/4AC*AC/2
216=3/4AC²/2
432=3/4AC²
AC²=432*4/3
AC²=576
AC=√576
AC=24(cm);
AB=3/4*24
AB=18(cm);
BC=√(24²+18²)=√(576+324)=√900=30(cm);
P=AB+AC+BC;
P=18+24+30=72(cm);

AD=AB*AC/BC;
AD=18*24/30=14,4(cm);

AB²=BD*BC
18²=BD*30
324=BD*30
BD=324/30
BD=10,8(cm);

AD²=BD*CD
(144/10)²=108/10*CD
CD(144/10)²*10/108
CD=19,2(cm).

Raspuns:a)P=72cm;
               b)AD=14,4cm;
               c)BD=10,8cm
                 CD=19,2cm.
Bafta!