Question

In triunghiul dreptunghic ABC m(A)=90°, se stie ca AB/AC=3/4,iar inaltimea AD=24 cm,
D apartine (BC). Aflati:
a) Perimetrul triunghiului
b) Aria triunghiului

Answer 1

AB/AC=3/4 ⇒ AB/3=AC/4=k ⇒AB=3k   AC=4k   
ΔABC TP⇒ BC²=Ab²+AC²=(3k)²+(4k)²=9k²+16k²=25k²⇒BC=5k   
AD= (AB×AC)/BC=(3k×4k)/5k=12k²/5k=12k/5=24 ⇒k=(24×5)/12=10  
⇒AB=3k=3×10=30   AC=4k=4×10=40    BC=5k=5×10=50        
 P= AB+AC+BC=30+40+50=120            
A= AB×AC/2= 30×40/2=600