To avoid a pond, Tom must walk 10 meters south and 24 meters east. To the nearest meter, how many meters would be saved if it were possible to walk through the pond?
10^2 + 24^2 = C^2
100 + 576 + C^2
C^2 = 676
C^2 = SQRT of 676 or 26 meters
not quite. You figured the straight-line distance, but that does not answer the question.
Read it again carefully.
To find out how many meters would be saved if it were possible to walk through the pond, we first need to determine the distance Tom would have to walk if he went around the pond.
Given that Tom needs to walk 10 meters south and 24 meters east, we can use the Pythagorean theorem to calculate the distance he would have to walk.
The Pythagorean theorem states that in a right triangle, the square of the hypotenuse (denoted as C) is equal to the sum of the squares of the two other sides.
So, in this case, let's consider the distance Tom would have to walk as the hypotenuse (C), which we need to find. The two other sides are 10 meters (south) and 24 meters (east).
Using the Pythagorean theorem, we can write the equation:
10^2 + 24^2 = C^2
Simplifying this equation, we have:
100 + 576 = C^2
676 = C^2
To find the value of C, we take the square root of both sides:
C = √676
C = 26 meters
So, the distance Tom would have to walk to avoid the pond is approximately 26 meters.
To calculate the meters saved by walking through the pond, we subtract the distance Tom would have to walk around the pond (26 meters) from the direct distance through the pond (hypotenuse). In this case, that would be 26 minus the sum of 10 (south) and 24 (east).
Meters saved = 26 - (10 + 24)
Meters saved = 26 - 34
Meters saved = -8 meters (negative value indicates that going through the pond is longer)
Therefore, if it were possible to walk through the pond, it would add an extra distance of 8 meters instead of saving any meters.