Chapter 9.4, Problem 13PSB

To determine

To Calculate: The distance covered if he walked straight.

Answer to Problem 13PSB

Thedistance covered if he walked straight is $2\sqrt{5}\left(\sqrt{2}+1\right)$

Explanation of Solution

Given information:

AL Capone walked $2$ km north

  $6$ km west

  $4$ km north and

  $2$ km west.

Formula used:

Here, we are using Pythagoras theorem.

  ${\left(Hypotenuse\right)}^2={\left(perpendicular\right)}^2+{\left(base\right)}^2$

Calculation:

  

Here, the formula is

  ${\left(Hypotenuse\right)}^2={\left(perpendicular\right)}^2+{\left(base\right)}^2$

  $A{D}^2=2^2+4^2$

  $A{D}^2=4+16$

  $AD=2\sqrt{5}$

And, $D{C}^2=6^2+2^2$

  $D{C}^2=36+4$

  $DC=2\sqrt{10}$

Here, Go straight is AD + DC

  →$2\sqrt{5}+2\sqrt{5}\times 2$

  →$2\sqrt{5}\left(\sqrt{2}+1\right)$

Conclusion: Hence,the distance covered if he walked straight is $2\sqrt{5}\left(\sqrt{2}+1\right)$