Answer:
The path is 17 ft long.
Step-by-step explanation:
Let c represent the length of the hypotenuse of a right triangle, and let a and b represent the lengths of its legs, as pictured in the image below.
The relationship involving the legs and hypotenuse of the right triangle, given by
[tex]a^2+b^2=c^2[/tex]
is called the Pythagorean Theorem.
The diagonal of the rectangle is equivalent to finding the length of the hypotenuse of a right triangle with sides 8 feet wide and 15 feet long.
Applying the Pythagoras' Theorem, we get
[tex]d^2=(8)^2+(15)^2\\d^2=64+225\\d^2=289\\d=\sqrt{289}=17[/tex]
Technically, there are two answers to [tex]d^2=289[/tex], i.e., d = 17 or d = -17. However, d represents the hypotenuse of the right triangle and must be non-negative. Hence, we must choose d = 17.
The path is 17 ft long.
