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You need to walk to your friend’s house but are trying to avoid a pond. You must walk 34 meters south and 41 meters east. To the nearest meter, how many meters would be saved if it were possible to walk through the pond?

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We can use the Pythagorean theorem to find the distance saved if it were possible to walk through the pond in a straight line. The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse (c) is equal to the sum of the squares of the lengths of the other two sides (a and b):

c^2 = a^2 + b^2

In this case, a = 34 meters (south) and b = 41 meters (east). We can plug these values into the theorem to find the length of the hypotenuse, which represents the straight-line distance through the pond:

c^2 = (34)^2 + (41)^2
c^2 = 1156 + 1681
c^2 = 2837
c = sqrt(2837)
c ≈ 53.26 meters

Now, we can find the distance saved by subtracting the straight-line distance through the pond from the total distance walking around it:

Distance saved = (34 + 41) - 53.26
Distance saved = 75 - 53.26
Distance saved ≈ 21.74 meters

To the nearest meter, approximately 22 meters would be saved if it were possible to walk through the pond.
User Xabhi
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