1) Jaden walked on a path on which he only made right angle turns. He went \(540\) meters south, then \(1266\) meters west, then \(1070\) meters south and finally \(473\) meters west. If he ran directly straight back to his starting point from his ending spot, then how far did he walk and how far did he run?
4) In a right triangle, the lengths of the medians to the legs of the triangle are \(\sqrt{601}\) and \(2\sqrt{61}\). Find the length of the hypotenuse of this triangle.
5) An engineer is designing an escalator for a new mall being constructed. In the original requested plan, the height between the floors was \(25\) feet and the engineer designed an escalator that was \(81\) feet long. The architect for the project changed his mind and requested that the escalator be designed where the base would be half the length. What length will be needed for the escalator now?
6) Given an isosceles triangle whose altitude to the base is \(12\) in and perimeter is \(36\) in, find the length of a leg.
7) Three sides of a triangle are \(12\), \(22\), and \(x\). What are the restrictions on \(x\) if the triangle is an obtuse triangle?
8) Three sides of a triangle are \(15\), \(8\), and \(x\). What are the restrictions on \(x\) if the triangle is an acute triangle?
7) Three sides of a triangle are \(12\), \(22\), and \(x\). What are the restrictions on \(x\) if the triangle is an obtuse triangle?
8) Three sides of a triangle are \(15\), \(8\), and \(x\). What are the restrictions on \(x\) if the triangle is an acute triangle?