The distance x, in kilometers, we need to find is the hypotenuse of the right triangle with legs measuring 50 km and 130 km.
Thus, we can use the Pythagorean Theorem to find x, in kilometers:
[tex]\begin{gathered} x^{2}=50^{2}+130^{2} \\ \\ x^{2}=2500+16900 \\ \\ x^{2}=19400 \\ \\ \sqrt[]{x^{2}}=\sqrt[]{19400} \\ \\ x\cong139.3 \end{gathered}[/tex]
Therefore, the distance from the table to the house is approximately 139.3 km.
