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
Step 1: Convert all dimensions to centimetres. Garden length: 24~m = 24 × 100 = 2400~cm Garden width: 14~m = 14 × 100 = 1400~cm Path width: 1~m = 1 × 100 = 100~cm Tile side length: 20~cm Step 2: Calculate total dimensions of garden plus path. Total length: 2400~cm + 2 × 100~cm = 2600~cm Total width: 1400~cm + 2 × 100~cm = 1600~cm Step 3: Calculate area of total region. 2600~cm × 1600~cm First, 2600 × 1000 = 2\,600\,000~cm^2 Then, 2600 × 600 = 1\,560\,000~cm^2 Total area: 2\,600\,000~cm^2 + 1\,560\,000~cm^2 = 4\,160\,000~cm^2 Step 4: Calculate garden area. 2400~cm × 1400~cm First, 2400 × 1000 = 2\,400\,000~cm^2 Then, 2400 × 400 = 960\,000~cm^2 Garden area: 2\,400\,000~cm^2 + 960\,000~cm^2 = 3\,360\,000~cm^2 Step 5: Calculate path area. 4\,160\,000~cm^2 - 3\,360\,000~cm^2 = 800\,000~cm^2 Step 6: Calculate area of one tile. 20~cm × 20~cm = 400~cm^2 Step 7: Calculate number of tiles required. 800\,000~cm^2400~cm^2 800\,000 ÷ 400 = 2000 The number of tiles required is 2000.