Question

In triunghiul dreptunghic ABC,m(<A)=90*,se stie ca $\frac{AB}{AC}$ = $\frac{3}{4}$ ,iar inaltimea AD =24 cm,D∈(BC).Calculati:
a)Perimetrul triunghiului
b)Aria triunghiului

Answer 1

ΔABC(<A)=90
AD_l_BC
BC²=AB²+AC²=(3k)²+(4k)²=9k²+16k²=25k²⇔BC=5k
AD=AB*AC/BC=3k*4k/5k=12k/5
12k/5=24
k=5*24/12
k=5*2=10
AB=3*10=30
AC=4*10=40
BC=5*10=50
PΔABC=30+50+50=120cm
AΔABC=AB*AC/2=30*40/2=30*20=600cm