Question

11 peter attached one end of his pet’s 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 and apply Pythagorean theorem

We have a right - triangle with legs \(a = 5\) ft and \(b=12\) ft. The Pythagorean theorem is \(c^{2}=a^{2}+b^{2}\), where \(c\) is the hypotenuse (length of the leash).
\[c^{2}=5^{2}+12^{2}\]

Step2: Calculate \(a^{2}\) and \(b^{2}\)

\[5^{2}=25\] and \[12^{2}=144\]
So, \(c^{2}=25 + 144\)

Step3: Find \(c^{2}\)

\[c^{2}=169\]

Step4: Solve for \(c\)

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

Answer:

D. 13 feet