Question

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

Answer 1

ΔABC, mas<A=90
AD _|_ BC
AD-h

BC²=AB² +AC² = (3k)² + (4k)² =9k² +16k² =25k²  =>BC=5k

AD=24

AD=AB*AC/BC= 3k*4k/5k= 12k/5

12k/5=24

k=5*24/12

k=5*2

k=10

AB=3*10=30
AC=4*10=40
BC=5*10=50

P=30+40+50= 120

A ΔABC= AB*AC/2= 30*40/2=  30*20= 600