This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.
ScanSolve AI Answer
Here are the solutions to your questions: 1. Calculate map length a) Scale 1:100, Actual distance = 7 km Step 1: Convert the actual distance from kilometres to centimetres. 1 km = 1000 m 1 m = 100 cm So, 1 km = 1000 × 100 cm = 100000 cm. Actual distance = 7 km = 7 × 100000 cm = 700000 cm. Step 2: Use the scale to find the map length. A scale of 1:100 means 1 cm on the map represents 100 cm in actual distance. Map Length = Actual DistanceScale Factor Map Length = 700000 cm100 Map Length = 7000 cm Step 3: Convert the map length to meters if desired, but the question implies cm. The map length is 7000 cm b) Scale 1 cm = 0.5 km, Actual distance = 8 km Step 1: Use the given verbal scale. The scale states that 1 cm on the map represents 0.5 km in actual distance. Step 2: Determine how many 0.5 km segments are in 8 km. Number of segments = 8 km0.5 km/cm Number of segments = 16 Step 3: Multiply the number of segments by 1 cm to find the map length. Map Length = 16 × 1 cm Map Length = 16 cm The map length is 16 cm 3. Calculate the suitable scale a) Map length = 8 cm, Actual distance = 20 km Step 1: Convert the actual distance from kilometres to centimetres. Actual distance = 20 km = 20 × 100000 cm = 2000000 cm. Step 2: Set up the ratio of map length to actual distance. Scale = Map Length : Actual Distance Scale = 8 cm : 2000000 cm Step 3: Simplify the ratio by dividing both sides by the map length (8 cm) to get a 1:X scale. Scale = (8)/(8) : (2000000)/(8) Scale = 1 : 250000 The suitable scale is 1:250000 b) Map length = 5.6 cm, Actual distance = 290 km Step 1: Convert the actual distance from kilometres to centimetres. Actual distance = 290 km = 290 × 100000 cm = 29000000 cm. Step 2: Set up the ratio of map length to actual distance. Scale = Map Length : Actual Distance Scale = 5.6 cm : 29000000 cm Step 3: Simplify the ratio by dividing both sides by the map length (5.6 cm). Scale = (5.6)/(5.6) : (29000000)/(5.6) Scale = 1 : 5178571.428... Step 4: Round the scale factor to a reasonable whole number, typically for map scales. Scale ≈ 1 : 5178571 The suitable scale is 1:5178571 c) Map length = 4 cm, Actual distance = 2 km Step 1: Convert the actual distance from kilometres to centimetres. Actual distance = 2 km = 2 × 100000 cm = 200000 cm. Step 2: Set up the ratio of map length to actual distance. Scale = Map Length : Actual Distance Scale = 4 cm : 200000 cm Step 3: Simplify the ratio by dividing both sides by the map length (4 cm). Scale = (4)/(4) : (200000)/(4) Scale = 1 : 50000 The suitable scale is 1:50000 Last free one today — make it count tomorrow, or type /upgrade for unlimited.