Question

11
peter attached one end of his pets leash to the top of a 5 - foot - tall fence post, as shown in the figure below.
the pet is 12 feet away from the base of the fence post. how long is the leash, to the nearest foot?
a. 4 feet
b. 7 feet
c. 11 feet
d. 13 feet
e. 17 feet

Explanation:

Step1: Identify right - triangle

The situation forms a right - triangle with legs \(a = 5\) ft and \(b=12\) ft, and the leash is the hypotenuse \(c\).

Step2: Apply Pythagorean theorem

The Pythagorean theorem is \(c^{2}=a^{2}+b^{2}\). Substitute \(a = 5\) and \(b = 12\) into the formula: \(c^{2}=5^{2}+12^{2}=25 + 144=169\).

Step3: Solve for \(c\)

Take the square root of both sides: \(c=\sqrt{169}=13\).

Answer:

D. 13 feet