The total calories that are burned by Ashton to cover the entire journey are 1890 calories.
A Pythagoras theorem gives us the relationship between the three sides of a right-angled triangle.
[tex]\rm (Hypotenuse)^2=(Base)^2+(Perpendicular)^2[/tex]
We know that Ashton's journey started by running 4 miles towards the east, later on, he ran 3 miles towards the north and then diagonally back towards the home, if we draw the diagram of the path taken by him we will realize that, Ashton made a triangular path.
As the two sides of the triangle are known and the triangle is a right-angled triangle, therefore, according to the Pythagoras theorem,
[tex]\rm (Hypotenuse)^2=(Base)^2+(Perpendicular)^2\\\\AC^2 = AB^2 + BC^2\\\\AC^2 = 4^2 + 3^2\\\\AC\ = 5[/tex]
Thus, the length of the third side of the triangle is 5 miles.
Now, as we know all the three sides of the triangle, the perimeter of the triangle can be found, which is the actual distance that is covered by Ashton.
Perimeter of the triangle = 5 + 4 + 9
= 18 miles
We know that for each mile covered by Ashton, he burned 105 calories, therefore, the total number of calories that are burned by Ashton while running along the perimeter of the triangle,
Number of calories = 18 miles x 105 calories/mile
= 18 x 105
= 1,890 calories
Hence, the total calories that are burned by Ashton to cover the entire journey are 1890 calories.
Learn more about Pythagoras Theorem:
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