a boy walks 2 miles east from his home ans then turns south and walks an additional 1.5 mile. how far is he from his home?

2^2+1.5^2=6.25

sqrt(6.25)= 2.5 miles

To find how far the boy is from his home, we can use Pythagoras' theorem, which states that in a right-angled triangle, the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.

In this case, the boy's home, the two-mile distance he walked east, and the 1.5-mile distance he walked south form a right-angled triangle. Let's call the distance the boy is from his home "d."

To solve for "d," we can consider the two sides of the triangle:

1. The distance the boy walks east: This is the base of the triangle and is equal to 2 miles.
2. The distance the boy walks south: This is the height of the triangle and is equal to 1.5 miles.

Now, we can use Pythagoras' theorem to find the hypotenuse, which is the distance d from the boy's home:

d^2 = (2^2) + (1.5^2)
d^2 = 4 + 2.25
d^2 = 6.25

To solve for d, we take the square root of both sides:

d = √6.25
d ≈ 2.5

Therefore, the boy is approximately 2.5 miles away from his home.