Question

the diagram shows three different bicycle routes taken by frank, alexis, and juan to get to the electronics store. according to the diagram, juan traveled kilometers. electronics store frank - 8 kilometers alexis - 6 kilometers juan -? kilometers

Explanation:

Step1: Identify right - triangle

The paths form a right - triangle with sides 6 km and 8 km, and Juan's path is the hypotenuse.

Step2: Apply Pythagorean theorem

Let \(a = 6\), \(b = 8\), and the hypotenuse \(c\). The Pythagorean theorem is \(c=\sqrt{a^{2}+b^{2}}\).
So \(c=\sqrt{6^{2}+8^{2}}=\sqrt{36 + 64}=\sqrt{100}\).

Step3: Calculate the value of \(c\)

\(\sqrt{100}=10\).

Answer:

10