Problemas
2. Two joggers run 8 miles north and then 5 miles west.What is the shortest distance, to the nearest mile, they must run to travel to return to their starting point? Draw a picture!
Roztwór
Juan
professionell · Tutor durante 6 años
4.1
(180 Votos)
Respuesta
The shortest distance they must run to return to their starting point is 10 miles.
Explicación
## Step 1The problem describes a right triangle, where the joggers run 8 miles north and then 5 miles west. The shortest distance they must run to return to their starting point is the hypotenuse of this right triangle.## Step 2We can use the Pythagorean theorem to solve this problem. The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides. This can be written as:###
where
and
are the lengths of the two legs of the triangle, and
is the length of the hypotenuse.## Step 3In this case,
miles (the distance run north) and
miles (the distance run west). We can substitute these values into the Pythagorean theorem to find
:###
## Step 4The square root of 89 is approximately 9.43. However, the problem asks for the nearest mile, so we round this to 10 miles.