Question

MNPQ-trapez, MN||PQ , MN=45cm,PQ=15 cm,NP=24cm,MQ=18cm MQ intersectat NP=T.Aflati:a. Perimetrul triunghiului TQP si b.Cat la % reprezinta aria triunghiului TQP din aria trapezului MNPQ

Answer 1

Conf Teoremei Thales(derivata ei) TQ/QM=TP/PN=QP/MN
TQ/QM=QP/MN; ⇒TQ=QM·QP/MN ⇒TQ=18·15/45=6cm
TP/PN=QP/MN ⇒TP=PN·QP/MN ⇒TP=24·15/45=8cm.
Permetrul tr TQP=QP+TQ+TP=15+6+8=29cm
Conform T Thales(derivata ei) inaltimea triunghiuluiTQP, fie ea TR, si a trapezului MNPQ, fie ea RS (sunt desenate in prelungire), formeaza  relatia TR/RS=QP/MN
Aria MNPQ=(MN+PQ)·RS/2=(45+15)·RS/2=30·RS
Aria TPQ=QP·TR/2=15·TR/2
Notam raportul lor cu Rap
Rap=(15TR/2)/30RS
Rap=TR/4RS
Inlocuim TR/RS=QP/MN
Rap=QP/4MN
Rap%=100·15/4·45=100/12=8,0(3)%