Question

Un trapez dreptunghic are bazele de 21 cm si 5 cm, iar inaltimea de 10 cm. La ce distanta de baza mare se intersecteaza laturile neparalele ale trapezului?

Answer 1

Fie ABCD ; AD║BC , AD<BC , AB⊥BC si AB∩DC={F} . Daca AD║BC prin Teorema fundamentala a asemanarii ⇒ ΔFAD asemenea cu ΔFBC ⇒ FA/FB= AD/BC⇒FA/(FA+10)=5/21⇒21FA=5FA+50 |-5FA⇒16FA=50⇒FA=50/16=25/8  =3,125 ⇒ FB=FA+AB=3,125cm+10cm=13,125cm ⇒d(F;BC)=FB=13,125cm .