Vector Algebra

Let $\mathbf{A}_1+\mathbf{A}_2=5 \mathbf{A}_3, \mathbf{A}_1-\mathbf{A}_2=3 \mathbf{A}_3, \mathbf{A}_3=2 \hat{\mathbf{i}}+4 \hat{\mathbf{j}}$, then $\frac{\left|\mathbf{A}_1\right|}{\left|\mathbf{A}_2\right|}$ is