Question

Fie ABCD un trapez isoscel,AB paralela cu CD,AB=12 cm,BC=10 cm si CD=24 cm.Calculati lungimea inaltimii si lungimea diagonalelor.

Answer 1

vezi figura
BE=AF= h (inaltimi in trapezul isoscel ABCD)
ABEF=DREPTUNGHI
ΔADF=ΔBEC⇒DE=EC=(DC-EF)/2=(24-12)/2=6
in Δ dreptunghic BEC⇒ cf pitagora
BE²=BC²-EC²=10²-6²=100-36
BE=8
in Δ dreptunghic AFC⇒AC²=AF²+FC²=8²+18²=64+324=388
AC=DB=D (diag trap)=√388=2√97