Question

Se consideră trapezul dreptunghic ABCD cu AB || CD si ABC=60 grade , BC=6cm si CD= 3 cm. Daca M este mijlocul diagonalei AC, atunci....DM=?

Answer 1

Fie CE⊥AB

In ΔCEB dr in E, avem ∡B=60⇒ m(∡BCE)=30°⇒ 2EB=BC

EB=6:2=3cm

CD=AE=3cm⇒ AB=AE+EB=3+3=6cm

In ΔCEB aplicam Pitagora

BC²=CE²+EB²

36=CE²+9

CE=3√3 cm

In ΔAEC aplicam Pitagora

AC²=CE²+AE²

AC²=27+9=36

AC=6cm

In ΔADC dr in D, DM mediana ⇒ DM=AC:2=6:2=3cm