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: Identify the dimensions of the original photograph and calculate its area. The original photograph has a length (L_original) of 6 m and a width (W_original) of 5 m. The area of the original photograph (A_original) is: A_original = L_original × W_original = 6 m × 5 m = 30 m^2 This matches the student's calculation of A = 6 × 5 = 30. Step 2: Determine the linear scale factor from the student's previous work. From the student's work in part 'a', it is assumed that the linear scale factor (k) is 2. k = 2 Step 3: Calculate the dimensions of the enlarged photograph using the linear scale factor. New Length (L_enlarged) = L_original × k = 6 m × 2 = 12 m New Width (W_enlarged) = W_original × k = 5 m × 2 = 10 m This matches the student's calculation for the enlarged width. Step 4: Calculate the area of the enlarged photograph. The area of the enlarged photograph (A_enlarged) is: A_enlarged = L_enlarged × W_enlarged = 12 m × 10 m = 120 m^2 Step 5: Calculate the area scale factor (ASF). The area scale factor is the ratio of the area of the enlarged photograph to the area of the original photograph. ASF = A_enlargedA_original = 120 m^230 m^2 = 4 Alternatively, the area scale factor is the square of the linear scale factor (k^2). ASF = k^2 = 2^2 = 4 The area scale factor is 4. Last free one today — make it count tomorrow, or type /upgrade for unlimited.