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?
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.
To find the length of the track, we can use the Pythagorean theorem.
Let's assume the length of the track is x yards.
The width of the track forms one side of a right triangle with the diagonal, and the length of the track forms the other side. The diagonal is the hypotenuse of the right triangle.
According to the Pythagorean theorem, the square of the hypotenuse is equal to the sum of the squares of the other two sides.
In this case, we have:
x^2 + 5^2 = 13^2
Simplifying the equation, we get:
x^2 + 25 = 169
Subtracting 25 from both sides, we have:
x^2 = 144
Taking the square root of both sides, we get:
x = √144
Simplifying, we have:
x = 12
Therefore, the length of the track is 12 yards.