Questions: Ahmed walked around a regular pentagon-shaped path. He started at the point (shown in the figure), walked around it clockwise, and came back to it again. On which part of the path was he walking when he covered 35% of the distance?

Ahmed walked around a regular pentagon-shaped path. He started at the point (shown in the figure), walked around it clockwise, and came back to it again. On which part of the path was he walking when he covered 35% of the distance?

Transcript text: Ahmed walked around a regular pentagon-shaped path. He started at the point (shown in the figure), walked around it clockwise, and came back to it again. On which part of the path was he walking when he covered $35 \%$ of the distance?

Solution

Solution Steps

Step 1: Determine the Total Distance

The path is a regular pentagon, which means it has 5 equal sides. Let's denote the length of each side as $ s $. Therefore, the total distance Ahmed walked around the pentagon is $ 5s $.

Step 2: Calculate 35% of the Total Distance

To find out how much distance Ahmed covered when he walked 35% of the total distance, we calculate: \[ 0.35 \times 5s = 1.75s \]

Step 3: Determine the Position on the Path

Since each side of the pentagon is $ s $, walking 1.75 sides means Ahmed walked 1 full side and 0.75 of the next side.

He starts at point $ a $.
After walking 1 side, he reaches point $ b $.
After walking an additional 0.75 of the next side, he is 0.75 of the way from $ b $ to $ c $.

Thus, Ahmed is on the path between points $ b $ and $ c $.