Question

Two joggers run 5km north and then 12km west. What is the shortest distance to the nearest tenth of a kilometer, they must travel to return to their starting point?

Answer 1

Answer:

13km

Step-by-step explanation:

first draw it 5 up (for north) and 12 to the left(for west) , then connect end points of both straight lines.

As you can see from the attachment, right angle triangle is formed by the given information, and we have to find hypotenuse.

lets apply Pythagoras theorem to determine the shortest distance

$a^{2} +b^{2} =c^{2}$

where a=12km and b=5km

$12^{2} +5^{2} =c^{2}$

$144+25=c^{2}$

$169=c^{2}$ (taking square root on both sides)

c= 13 km.

So, 13 km is the shortest distance

Answer 2

Answer: The shortest distance that they must travel to return to their starting positions is 13 miles

Step-by-step explanation:

 If the joggers jogged 5km due north and later jogged 12km due west; they formed a right angle triangle without their knowledge. If this action by the joggers consequently resulted in a right angle triangle, we can calculate the shortest distance that they must travel to return to their starting position by using the Pythagoras formula. The Pythagoras formula then is:

$Hyp^{2}$ = $Opp^{2} + adj^{2}$

   In this case, the path the joggers took as they jogged 5km due north is the opposite; The path they took as they jogged due west is the adjacent. The straight line distance from their starting positions is the hypotenuse.

   This simply means that the opposite for this calculation is 5km and the adjacent is the 12km path they followed as they  travelled due west.

The hypotenuse is now the variable to that will be determined or calculated. We can  use "b" to represent the hypotenuse in the calculation.

        $b^{2} =5^{2} +12^{2}$

        $b^{2}$   = 25 + 144

         $b^{2}$= 169

         b = $\sqrt{169$

         b = 13

Therefore, the shortest distance that they must travel in order to return to their starting positions is 13 miles