Question

1) In triunghiul dreptunghic ABC,m(<A)=90,se stie ca BC=12√13cm,iar $\frac{AB}{AC} = \frac{2}{3}$.Calculati:
a) lunigimile catetelor triunghiului dat:
b) aria triunghiului ABC.

Answer 1

ΔABC, mas<A=90

AB/AC= 2/3

AB/2=AC/3=k
AB=2k
AC=3k

BC²=AB²+AC²

(12√13)²=(2k)²+ (3k)²

1872=4k² +9k²

1872=13k²

k²=144 =>k=12

AB=2*12=24
AC=3*12=36

b)A ΔABC=AB*AC/2=  24*36/2= 12*36= 432