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's the solution for problem 1: To find the percentage error, we use the formula: Percentage Error = |Measured Value - True Value|True Value × 100\% Given: True length (L_T) = 18.6 m True width (W_T) = 12.4 m Measured length (L_M) = 18.2 m Measured width (W_M) = 12.7 m i. Measured length Step 1: Calculate the absolute error in length. Error in length = |L_M - L_T| = |18.2 - 18.6| = |-0.4| = 0.4 m Step 2: Calculate the percentage error in length. Percentage Error (Length) = (0.4)/(18.6) × 100\% ≈ 2.1505\% Rounded to two decimal places: 2.15% ii. Calculated perimeter Step 1: Calculate the true perimeter and measured perimeter. P_T = 2(L_T + W_T) = 2(18.6 + 12.4) = 2(31.0) = 62.0 m P_M = 2(L_M + W_M) = 2(18.2 + 12.7) = 2(30.9) = 61.8 m Step 2: Calculate the absolute error in perimeter. Error in perimeter = |P_M - P_T| = |61.8 - 62.0| = |-0.2| = 0.2 m Step 3: Calculate the percentage error in perimeter. Percentage Error (Perimeter) = (0.2)/(62.0) × 100\% ≈ 0.3226\% Rounded to two decimal places: 0.32% iii. Calculated area Step 1: Calculate the true area and measured area. A_T = L_T × W_T = 18.6 × 12.4 = 230.64 m^2 A_M = L_M × W_M = 18.2 × 12.7 = 231.14 m^2 Step 2: Calculate the absolute error in area. Error in area = |A_M - A_T| = |231.14 - 230.64| = 0.50 m^2 Step 3: Calculate the percentage error in area. Percentage Error (Area) = (0.50)/(230.64) × 100\% ≈ 0.2168\% Rounded to two decimal places: 0.22% Got more? Send 'em!