قائم‌الزاویه $A\overset{\Delta }{\mathop{B}}\,C\Rightarrow A{{C}^{2}}=A{{B}^{2}}+B{{C}^{2}}\Rightarrow {{5}^{2}}=A{{B}^{2}}+{{3}^{2}}\Rightarrow AB=4$ $DE\parallel BC\Rightarrow \frac{x}{AB}=\frac{y}{BC}=\frac{AE}{AC}$ $\Rightarrow \frac{x}{4}=\frac{y}{3}=\frac{5-2}{5}\Rightarrow \frac{x}{4}=\frac{3}{5}\Rightarrow x=\frac{12}{5}$ $\Rightarrow \frac{y}{3}=\frac{3}{5}\Rightarrow y=\frac{9}{5}$ $x+y=\frac{12}{5}+\frac{9}{5}=\frac{21}{5}=4/2$