From his home, Zach would have to walk 5.6 kilometers north to get to his friend Nancy's house and 7 kilometers east to get to his friend Wendy's house. One day, Zach walked from his home to Wendy's house. Together, Wendy and Zach cut directly through the field that separated them from Nancy's house. When they finished playing at Nancy's, Zach walked back home. In all, how far did Zach walk? If necessary, round to the nearest tenth.
Question
From his home, Zach would have to walk 5.6 kilometers north to get to his friend Nancy's house and 7 kilometers east to get to his friend Wendy's house. One day, Zach walked from his home to Wendy's house. Together, Wendy and Zach cut directly through the field that separated them from Nancy's house. When they finished playing at Nancy's, Zach walked back home. In all, how far did Zach walk? If necessary, round to the nearest tenth.
Solution
To solve this problem, we need to find the distance Zach walked from Wendy's house to Nancy's house. This can be found using the Pythagorean theorem because the path Zach took from his house to Wendy's, then to Nancy's, forms a right triangle.
Step 1: Use the Pythagorean theorem, which is a^2 + b^2 = c^2. Here, a is the distance from Zach's house to Wendy's house (7 km), and b is the distance from Zach's house to Nancy's house (5.6 km).
Step 2: Substitute the given values into the formula: (7)^2 + (5.6)^2 = c^2.
Step 3: Calculate the squares: 49 + 31.36 = c^2.
Step 4: Add the results: 80.36 = c^2.
Step 5: Find the square root of both sides to solve for c. The square root of 80.36 is approximately 8.97 km. This is the distance Zach walked from Wendy's house to Nancy's house.
Step 6: Add the distances Zach walked: from his house to Wendy's (7 km), from Wendy's to Nancy's (8.97 km), and from Nancy's back to his house (5.6 km).
Step 7: 7 km + 8.97 km + 5.6 km = 21.57 km.
So, Zach walked a total of approximately 21.6 km (rounded to the nearest tenth).
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