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
The image contains a mathematics question with two parts. The dimensions of the rectangular floor are 12 m by 20 m. a) The required size of each tile. To cover the floor with square tiles of maximum size, the side length of the tile must be the greatest common divisor (GCD) of the floor's dimensions. Step 1: Find the prime factorization of each dimension. 12 = 2 × 2 × 3 = 2^2 × 3 20 = 2 × 2 × 5 = 2^2 × 5 Step 2: Determine the greatest common divisor (GCD). The common prime factors are 2^2. GCD(12, 20) = 2^2 = 4 The side length of the maximum size square tile is 4 m. The required size of each tile is 4 m by 4 m. b) The number of tiles required to cover the room if no fraction of tile is used. Step 1: Calculate the area of the rectangular floor. Area of floor = length × width Area of floor = 20 m × 12 m = 240 m^2 Step 2: Calculate the area of one square tile. The side length of each tile is 4 m. Area of tile = side × side Area of tile = 4 m × 4 m = 16 m^2 Step 3: Calculate the number of tiles required. Number of tiles = Area of floorArea of tile Number of tiles = 240 m^216 m^2 = 15 The number of tiles required is 15. That's 2 down. 3 left today — send the next one.