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
Welcome back KIMBE — missed you this week. a) To find the scale factor of enlargement from Rectangle P to Rectangle Q, we divide a dimension of Rectangle Q by the corresponding dimension of Rectangle P. Step 1: Calculate the scale factor using the lengths. Scale factor = Length of Rectangle QLength of Rectangle P = 15 cm6 cm Scale factor = (15)/(6) = (5)/(2) = 2.5 The scale factor is (5)/(2) or 2.5. b) Since the rectangles are similar, the ratio of their widths must be equal to the scale factor. Step 1: Set up the proportion for the widths. Width of Rectangle QWidth of Rectangle P = Scale factor (x)/(4 cm) = (5)/(2) Step 2: Solve for x. x = (5)/(2) × 4 cm x = 5 × 2 cm x = 10 cm The value of x is 10 cm. c) The area of a rectangle is calculated by multiplying its length by its width. Step 1: Calculate the area of Rectangle P. Area of Rectangle P = Length × Width Area of Rectangle P = 6 cm × 4 cm Area of Rectangle P = 24 cm^2 The area of Rectangle P is 24 cm^2. d) Calculate the area of Rectangle Q using its length and the value of x found in part (b). Step 1: Calculate the area of Rectangle Q. Area of Rectangle Q = Length × Width Area of Rectangle Q = 15 cm × 10 cm Area of Rectangle Q = 150 cm^2 The area of Rectangle Q is 150 cm^2. Send me the next one 📸