Question

Triunghiul dreptunghic ABC , m(<A)=90°, AD⊥BC,D apartine (BC) are Ab supra Ac = 3 supra 4 si aria egala cu 216cm².Aflati:  a)perimetrul triunghiului
b) lungimea inaltimii AD;
c) lungimile segmentelor BD si CD
Ajutor!!!

Answer 1

AB/AC=3/4
AB=3k
AC=4k
AC*AB/2=216
3k*4k/2=216
6k²=216
k²=36
k=6
AB=3*6=18 cm
AC=4*6=24 cm
BC=√(18²+24²)=√(324+576)=√900=30 cm
P=18+24+30=72 cm
A=BC*AD/2
AD=2*216/30=14,4 cm
AB²=BD*BC
324=BD*30
BD=10,8 cm
AC²=DC*BC
576=DC*30
DC=19,2 cm