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.
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Here are the solutions to the remaining questions from the image: Question 7: The perimeter of a square whose area is 576 m^2 is: Step 1: Find the side length of the square. The area of a square (A) is given by the formula A = s^2, where s is the side length. Given A = 576 m^2. s^2 = 576 m^2 To find s, take the square root of the area: s = sqrt(576 m)^2 s = 24 m Step 2: Calculate the perimeter of the square. The perimeter of a square (P) is given by the formula P = 4s. Substitute the side length s = 24 m: P = 4 × 24 m P = 96 m The correct option is C) 96 m. Question 8: A rectangular field measuring 100 m by 50 m was drawn on a scale of 1:1000. The drawing area was: Step 1: Determine the dimensions of the field on the drawing. The actual length (L) is 100 m and the actual width (W) is 50 m. The scale is 1:1000, meaning 1 unit on the drawing represents 1000 units in reality. Length on drawing (L_d): L_d = Actual LengthScale Factor = 100 m1000 = 0.1 m Width on drawing (W_d): W_d = Actual WidthScale Factor = 50 m1000 = 0.05 m Step 2: Calculate the area of the drawing. The area of a rectangle (A_d) is given by A_d = L_d × W_d. A_d = 0.1 m × 0.05 m A_d = 0.005 m^2 Step 3: Convert the area to square centimeters (cm^2) to match the options. We know that 1 m = 100 cm. Therefore, 1 m^2 = (100 cm)^2 = 10000 cm^2. A_d = 0.005 m^2 × 10000 cm^21 m^2 A_d = 50 cm^2 The correct option is A) 50 cm^2. That's 2 down. 3 left today — send the next one.