[tex]\it Fie \ \ BD=x,\ \ \ DC=x+40\\ \\ Teorema\ \ \hat\imath n\breve al\c{\it t}imii\ \Rightarrow x(x+40)=48^2 \Rightarrow x^2+40x-2304=0 \Rightarrow \\ \\ \Rightarrow x^2+40x+400-400-2304=0 \Rightarrow (x+20)^2-2704=0 \Rightarrow \\ \\ \Rightarrow (x+20)^2-52^2=0 \Rightarrow (x+20-52)(x+20+52)=0 \Rightarrow \\ \\ \Rightarrow (x-32)(x+72)=0 \Rightarrow x=32[/tex]
BD=32cm, DC = 32+40 = 72 cm, BC = 32 + 72= 104 cm
