Question

In dreptunghiul ABCD, BE _!_ AC, E apartine (AC). Daca EC=6cm si AE=24cm, calculati
P si A dreptunghiului. Va rogg!!

Answer 1

AC=6+24=30
avem asemanare intre triunghiurile ECB si BCA de unde

EC/BC=BC/CA
BC^2=EC*CA=6*30=180
BC=rad180=6*rad5

aplicam pitagora in triunghiul ABC
AB^2=AC^2-BC^2=30^2-(6*rad5)^2=900-180=720
AB=rad720=12*rad5

P=2(AB+BC)=2*18*rad5=36*rad5cm
A=AB*BC=6*rad5*12*rad5=360 cm^2