Question

In triunghiul dreptunghic ABC m(A=90°) se stiu AB=12 BC=24. Aratati ca aria lui ABC este mai mica decat 126 cm patrati

Answer 1

In tr. ABC
m(A)=90°
}=>(conform T.P.)
AC^2=BC^2 -AB^2
AC^2=24^2 -12^2=12^2(2^2 -1)=12^2 ·3
=> AC=12¬/3

A [ABC]=(AB·AC)/2=(12·12¬/3)/2=72¬/3 (cm^2)

72¬/3=¬/(72^2 ·3)=¬/15552
126=¬/126^2=¬/15876

¬/15552 < ¬/15876
=> A [ABC] < 126 cm^2