Question

edgars school is 15 kilometers west of his house and 8 kilometers south of his friend colettes house. every day, edgar bicycles from his house to his school. after school, he bicycles from his school to colettes house. before dinner, he bicycles home on a bike path that goes straight from colettes house to his own house. how far does edgar bicycle each day? kilometers

Explanation:

Step1: Analyze the triangle

The positions of Edgar's house, school, and Colette's house form a right triangle. The horizontal leg (west - east direction) is 15 km (from Edgar's house to school), and the vertical leg (north - south direction) is 8 km (from school to Colette's house? Wait, no. Wait, Edgar's school is 15 km west of his house, and 8 km south of Colette's house? Wait, re - reading: "Edgar's school is 15 kilometers west of his house and 8 kilometers south of his friend Colette's house". So the distance from Edgar's house to school is 15 km (west), school to Colette's house is 8 km (north, since school is south of Colette's house). Then the distance from Colette's house to Edgar's house is the hypotenuse of a right triangle with legs 15 km and 8 km.

First, find the distance from Colette's house to Edgar's house using the Pythagorean theorem: \(d=\sqrt{15^{2}+8^{2}}\)

Step2: Calculate the hypotenuse

\(15^{2}=225\), \(8^{2} = 64\), so \(15^{2}+8^{2}=225 + 64=289\). Then \(\sqrt{289}=17\) km. This is the distance from Colette's house to Edgar's house.

Now, let's list the distances Edgar bicycles:

• From Edgar's house to school: 15 km
• From school to Colette's house: 8 km
• From Colette's house to Edgar's house: 17 km

Step3: Sum the distances

Total distance \(=15 + 8+17\)

\(15+8 = 23\), \(23 + 17=40\) km.

Answer:

40