Two boys are running track. They decide to start in the northwest corner and go opposite directions around the rectangular track. If the width of the track is 5 yards and the diagonal is 13 yards, what is the length of the track?

Answer 1

Let the length of the track be $x$ yards. Since the diagonal divides the rectangle into two congruent right triangles, each with legs 5 yards and $x$ yards,
thus, by the Pythagorean Theorem, we have \[5^2+x^2=13^2.\] Simplifying the left side gives $25+x^2=169$. Subtracting 25 from both sides gives $x^2=144$. Since the length must be positive, $x=\boxed{12}$ yards.