Question

question 8. a student travels road c then road b to get to school and then takes road a home. what is the total distance traveled? (round your answer to the nearest hundredth)

Explanation:

Step1: Apply Pythagorean theorem

Let the length of Road C be \(x\) km. According to the Pythagorean theorem \(a^{2}+b^{2}=c^{2}\), where \(c = 10\) km (hypotenuse, Road A) and \(b=6\) km (Road B). So \(x^{2}+6^{2}=10^{2}\), which simplifies to \(x^{2}+36 = 100\). Then \(x^{2}=100 - 36=64\), and \(x = 8\) km.

Step2: Calculate total distance

The student travels Road C (\(8\) km) and Road B (\(6\) km) to school, then Road A (\(10\) km) back home. The total distance \(d=8 + 6+10\).

Answer:

\(24.00\) km