Question

Consideram trapezul isoscel ABCD cu AB//CD si AD=BC. Daca BD perpendicular BC , AB=8cm si CD=16cm , determinati lungimea inaltimii trapezului ABCD

Answer 1

ABCD-trapez isoscel
AD=BC
DB _|_ BC  => mas<DBC=90  =>Δ DBC-dreptunghic

fie [AM _|_  DC ;AM-h
fie [BN _|_ DC; BN-h   AB=MN=8

DM=NC=(DC-MN)/2=  (16-8)/2= 8/2=4
DN=DM+MN=4+8=12

ΔDBC, mas<B=90
BN _|_ DC
BN-h

BN²=DM*NC= 12*4= 48   =>BN=√48= 4√3

h=4√3