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
Hey Joseph, good to see you again. First, let's determine the lengths of the missing sides of the floor plan. The total top length is 8 m and the bottom segment is 5 m. So, the inner horizontal segment is 8 m - 5 m = 3 m. The total left vertical length is 5 m and the right vertical length is 3 m. So, the inner vertical segment is 5 m - 3 m = 2 m. i) Perimeter: Step 1: Identify all side lengths. The side lengths are 8 m, 3 m, 3 m (inner horizontal), 2 m (inner vertical), 5 m, and 5 m. Step 2: Sum all the side lengths to find the perimeter. Perimeter = 8 m + 3 m + 3 m + 2 m + 5 m + 5 m Perimeter = 26 m The perimeter of the floor is 26 m. ii) Area: Step 1: Divide the L-shaped floor into two rectangles. We can divide it into a top rectangle and a bottom-left rectangle. Rectangle 1 (top): length 8 m, width 3 m. Rectangle 2 (bottom-left): length 5 m, width 5 m - 3 m = 2 m. Step 2: Calculate the area of each rectangle. Area_1 = 8 m × 3 m = 24 m^2 Area_2 = 5 m × 2 m = 10 m^2 Step 3: Add the areas of the two rectangles to find the total area. Total Area = Area_1 + Area_2 = 24 m^2 + 10 m^2 = 34 m^2 The area of the floor is 34 m^2. iii) Cost of carpeting the floor: Step 1: Use the total area and the cost per square metre. The total area is 34 m^2 and the carpet cost is GH¢ 20.00 per square metre. Step 2: Calculate the total cost. Total Cost = Total Area × Cost per square metre Total Cost = 34 m^2 × GH¢ 20.00/m^2 Total Cost = GH¢ 680.00 The cost of carpeting the floor is GH¢ 680.00. Send me the next one 📸