Bryant's school is 2.2 kilometers west of his house and 2.3 kilometers south of his friend Zeke's house. Every day, Bryant bicycles from his house to his school. After school, he bicycles from his school to Zeke's house. Before dinner, he bicycles home on a bike path that goes straight from Zeke's house to his own house. How far does Bryant bicycle each day? If necessary, round to the nearest tenth.
Question
Bryant's school is 2.2 kilometers west of his house and 2.3 kilometers south of his friend Zeke's house. Every day, Bryant bicycles from his house to his school. After school, he bicycles from his school to Zeke's house. Before dinner, he bicycles home on a bike path that goes straight from Zeke's house to his own house. How far does Bryant bicycle each day? If necessary, round to the nearest tenth.
Solution
To solve this problem, we need to find the total distance Bryant bicycles each day.
First, we add the distance from Bryant's house to his school and from his school to Zeke's house:
2.2 km (house to school) + 2.3 km (school to Zeke's house) = 4.5 km
Then, we need to find the distance from Zeke's house to Bryant's house. This forms a right triangle, with the distance from the school to Zeke's house as one side, the distance from the school to Bryant's house as the other side, and the distance from Zeke's house to Bryant's house as the hypotenuse.
We can use the Pythagorean theorem to find this distance: a² + b² = c², where c is the hypotenuse.
So, (2.2 km)² + (2.3 km)² = c²
4.84 km² + 5.29 km² = c²
10.13 km² = c²
Taking the square root of both sides, we find that c = √10.13 km = 3.2 km (rounded to the nearest tenth).
So, the total distance Bryant bicycles each day is:
4.5 km + 3.2 km = 7.7 km.
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