Question

velma is a farmer who is building a pen for some animals. the first side of the pen is the longest, measuring 17 feet. the second side of the pen is 8 feet long. how long is the third side of the pen? round your answer to two decimal places. show your work here hint: to add the square root symbol (√□), type
oot\

Explanation:

Step1: Apply Pythagorean theorem

Let the third side be \(x\). According to Pythagorean theorem \(a^{2}+b^{2}=c^{2}\), where \(c = 17\) (hypotenuse) and \(a = 8\), \(b=x\). So \(x^{2}+8^{2}=17^{2}\), which can be rewritten as \(x^{2}=17^{2}-8^{2}\).

Step2: Calculate \(17^{2}-8^{2}\)

\(17^{2}=289\), \(8^{2} = 64\). Then \(x^{2}=289 - 64=225\).

Step3: Solve for \(x\)

\(x=\sqrt{225 - 64}=\sqrt{225-64}=\sqrt{165}\approx 12.85\)

Answer:

\(12.85\) feet