Question

A student leaves a physics classroom and walks 7 meters south to go to a water fountain. The student then walks 4 meters east to get to her math class. What is the girl's total distance traveled from the physics classroom to the math classroom? Do not type in the unit or the computer will mark your answer incorrect.

Answer 1

$\sqrt{65}$

Explanation

Step 1

Free body diagram

so, we have a rigth triangle, we can use the Pythagorean theorem to find the hypotensue.

the theorem that the sum of the squares on the legs of a right triangle is equal to the square on the hypotenuse (the side opposite the right angle),so

$\begin{gathered} a^2+b^2=c^2 \\ where\text{ c is the hypotenuse of the right triangle} \end{gathered}$

so

Let

$\begin{gathered} a=\text{ 7 m} \\ b=\text{ 4 m} \\ c=distance\text{ from physicsroom to math classroom} \end{gathered}$

now, replace and solve for c

$\begin{gathered} a^{2}+b^{2}=c^{2} \\ (7m)^2+(4m)^2=c^2 \\ (49)m^2+16(m^2)=c^2 \\ 65=c^2 \\ c=\sqrt{65\text{ }}\text{ meters} \end{gathered}$

therefore, the answer is

$\sqrt{65}$

I hope this helps you