Question 8 - Figure it out - Page 157-159 - Chapter 7 Class 8 - Area (Ganita Prakash II)

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Question 8 Gopal needs to carry water from the river to his water tank. He starts from his house. What is the shortest path he can take from his house to the river and then to the water tank? Roughly recreate the map in your notebook and trace the shortest path.This is a real-world application of the "mirror proof" from the previous pages! To find the absolute shortest path from the House, to the River, to the Water tank: Treat the river line as a mirror. Draw a "reflection" of the Water Tank on the opposite side of the river. Let's call it the Fake Tank. Take a ruler and draw a perfectly straight line from Gopal's House directly to the Fake Tank. The exact spot where your straight line crosses the river is the magic point. Gopal should walk straight to that point on the river, and then straight to the real water tank. That path will be the minimum perimeter! Let’s look at it in detail Drag the orange point on the river to find the shortest path! Drag the orange point on the river to find the shortest path! Heron's Shortest Path Back Next Step CURRENT PATH LENGTH Step 0: Try it yourself! Drag the orange point along the river. Watch the "Current Path Length" number. Try to find the absolute smallest number you can before clicking Next Step! Heron's Shortest Path Back Next Step CURRENT PATH LENGTH Step 1: The Magic Mirror To solve this math puzzle, we imagine the river is a giant, perfectly flat mirror.Heron's Shortest Path Back Next Step Drag the orange point on the river to find the shortest path! Fake Tank (Ref) P River CURRENT PATH LENGTH 458.7 m Step 2: The Fake Tank Look at the reflection! We "reflected" the real Water Tank across the river to create a Fake Tank. Because mirrors show exact distances, walking from the river to the Fake Tank is the exact same distance as walking to the Real Tank. Heron's Shortest Path Back Next Step Drag the orange point on the river to find the shortest path! Fake Tank (Res) Step 3: The Straight Line Now the problem is super easy! We just need to walk from the House to the Fake Tank. What is the absolute shortest path between two points? A perfectly straight line! (That's the pink dashed line). Drag the orange point on the river to find the shortest path! Heron's Shortest Path Back Next Step CURRENT PATH LENGTH 403.6 m Optimal Path Found! Step 4: The Perfect Spot The exact spot where our straight pink line crosses the river is the absolute best place to grab water (Point P). Minimum possible distance