Question

AJUTOOR!
Triunghiul dreptunghic ABC , masura unghiului A = 90 de grade , AD perpendicular pe BC , D apartine laturii BC , are $\frac{AB}{AC}$ = $\frac{3}{4}$ si aria egala cu 216 cm² .
Aflati :
a) perimetrul triunghiului
b) lungimea inaltimii AD
c) lungimile segmentelor BD si CD .

Answer 1

AB/AC=3/4
A=3k×4k/2
216=12k²/2
432=12k²
k²=36
k=6
AB=3x6=18cm
AC=4x6=24cm
BC=√(18²+24²)=√(324+576)=√900=30cm
P=18+24+30=72 cm
 A=BCxAD/2
216=30xAD/2
AD=216x2/30=14,4 cm
BD=√(18²-14,4)²=√(324-207,36)=√116,64=10,8cm
DC=√(24²-14,4)²=√(576-207,36)=√368,64=19,2cm