To get from point A to point B you must avoid walking through a pond. Toavoid the pond, you must walk 34 meters south and 41 meters east. To thenearest meter, how many meters would be saved if it were possible to walkthrough the pond?
Question
To get from point A to point B you must avoid walking through a pond. Toavoid the pond, you must walk 34 meters south and 41 meters east. To thenearest meter, how many meters would be saved if it were possible to walkthrough the pond?
Solution 1
To solve this problem, we need to use the Pythagorean theorem. This 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: a² + b² = c².
Here, walking 34 meters south and 41 meters east forms a right triangle. The distance saved by walking through the pond is the hypotenuse of this triangle.
Step 1: Square the lengths of the two sides: 34² = 1156 41² = 1681
Step 2: Add these two values together: 1156 + 1681 = 2837
Step 3: Take the square root of this sum to find the length of the hypotenuse: √2837 = 53.26 meters
So, if it were possible to walk through the pond, you would save approximately 53 meters. However, the problem asks for the answer to the nearest meter, so we round 53.26 to 53.
Therefore, you would save about 53 meters if it were possible to walk through the pond.
Solution 2
To solve this problem, we need to use the Pythagorean theorem. This 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: a² + b² = c².
Here, walking 34 meters south and 41 meters east forms a right triangle. The distance saved by walking through the pond is the hypotenuse of this triangle.
Step 1: Square the lengths of the two sides: 34² = 1156 41² = 1681
Step 2: Add these two values together: 1156 + 1681 = 2837
Step 3: Take the square root of this sum to find the length of the hypotenuse: √2837 = 53.26 meters
So, if it were possible to walk through the pond, you would save approximately 53 meters. However, the problem asks for the answer to the nearest meter, so we round 53.26 to 53.
Therefore, you would save about 53 meters if it were possible to walk through the pond.
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