Question

the club members hiked 8 kilometers north and 9 kilometers east, but then went directly home as shown by the dotted line. what is the distance they travel to get home?
home
kilometers
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Explanation:

Step1: Identify the triangle type

The path forms a right - triangle, with legs \(a = 8\) km and \(b=9\) km, and the distance home is the hypotenuse \(c\).

Step2: Apply Pythagorean theorem

The Pythagorean theorem states that for a right - triangle, \(c^{2}=a^{2}+b^{2}\). Substitute \(a = 8\) and \(b = 9\) into the formula:
\(c^{2}=8^{2}+9^{2}=64 + 81=145\)

Step3: Find the value of \(c\)

Take the square root of both sides: \(c=\sqrt{145}\approx12.04\) (we can also leave it as \(\sqrt{145}\), but if we calculate the approximate value, \(\sqrt{145}\approx12\) (or more precisely \(\sqrt{145}\approx12.04\))

Answer:

\(\sqrt{145}\) (or approximately \(12.04\))