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 are the solutions to the questions: 1.3 Determine the area of ACEG in the simplest possible form: Step 1: Identify the four smaller areas that make up the total area of ACEG. Area of ACEG = Area of ABJH + Area of BCDJ + Area of HJFG + Area of DEFJ. Step 2: Substitute the areas calculated in question 1.1. Area of ABJH = x^2 Area of BCDJ = 6x Area of HJFG = 4x Area of DEFJ = 24 Step 3: Sum these areas and simplify by combining like terms. Area of ACEG = x^2 + 6x + 4x + 24 Area of ACEG = x^2 + (6x + 4x) + 24 Area of ACEG = x^2 + 10x + 24 Units^2 1.4 Using your answer in 1.2 and 1.3 find the area of ACEG in the form ax^2 + bx + c = Step 1: Use the lengths of the sides of the large rectangle ACEG from question 1.2. AC = x+6 AG = x+4 Step 2: Multiply the lengths to find the area of ACEG. Area of ACEG = AC × AG = (x+6)(x+4) Step 3: Expand the product using the FOIL method (First, Outer, Inner, Last). (x+6)(x+4) = x · x + x · 4 + 6 · x + 6 · 4 = x^2 + 4x + 6x + 24 = x^2 + 10x + 24 1.5 (x+6)(x+4)= Step 1: Expand the product. (x+6)(x+4) = x^2 + 4x + 6x + 24 Step 2: Combine like terms. = x^2 + 10x + 24 2.1 Use the method you discovered in question 1 to determine the product of (x+8)(x+5) 2.1.1 Area of KLQR = Step 1: Identify the dimensions of rectangle KLQR. Length KL = x, Width KQ = x. Step 2: Calculate the area. Area of KLQR = KL × KQ = x × x = x^2 2.1.2 Area of LMPQ = Step 1: Identify the dimensions of rectangle LMPQ. Length LM = 8, Width LP = KQ = x. Step 2: Calculate the area. Area of LMPQ = LM × LP = 8 × x = 8x 2.1.3 Area of RQTS = Step 1: Identify the dimensions of rectangle RQTS. Length RQ = KL = x, Width RS = 5. Step 2: Calculate the area. Area of RQTS = RQ × RS = x × 5 = 5x 2.1.4 Area of QPTU = Step 1: Identify the dimensions of rectangle QPTU. Length QP = LM = 8, Width QT = RS = 5. Step 2: Calculate the area. Area of QPTU = QP × QT = 8 × 5 = 40 2.1.5 (x+8)(x+5)= Step 1: The product (x+8)(x+5) represents the total area of the large rectangle KLSU. Step 2: Sum the areas of the four smaller rectangles calculated above. (x+8)(x+5) = Area of KLQR + Area of LMPQ + Area of RQTS + Area of QPTU = x^2 + 8x + 5x + 40 Step 3: Combine like terms. = x^2 + 13x + 40 3 done, 2 left today. You're making progress.