Question

In triunghiul dreptunghic ABC, m(<A)=90 grade, se stie ca ABsupraAC = 3supra4,iar inaltimea AD=24cm. Calculati :
a)perimetrul triunghiului
b)aria triunghiului

Du 20 de puncte cui imi rezolva corect

Answer 1

AB/AC=3/4=k
AB=3k
AC=4k

Calculam,AD,cu,t.Pit.,din,ambele,triunghiuri,dr.Notam,cu,x,segm.CD,si,cu,y,segm.DB
AD²+x²=16k²
AD²+y²=9k²

Egalam,cei,doi,AD²
16k²-x²=9k²-y²
Stim,ca,x+y=5k=>x=5k-y
16k²-(5k-y)²=9k²-y²
16k²-25k²+10ky-y²=9k²-y²
-9k²-9k²=-10ky
-18k²=-10ky
-18k=-10y=>10y=18k
=>y=18k/10=9k/5
x=5k-9k/5=16k/5

AD²=16k/5x9k/5=144k²/25=576=>k²=576x25/144=100
=>k=10

=>AB=30
=>AC=40
=>BC=50

=>Perim=120
=>Aria=30x40/2=600cm²