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 perimeters for each shape. EXERCISE 35.2 Shape A: Step 1: Identify the dimensions of the rectangle. The sides are 27 mm and 19 mm. Step 2: Calculate the perimeter using the formula P = 2 × (length + width). P = 2 × (27 mm + 19 mm) P = 2 × (46 mm) P = 92 mm The perimeter of Shape A is 92 mm. Shape B: Step 1: Identify all side lengths. The given sides are 2 cm, 2.5 cm, 2 cm, 1.5 cm, and 4 cm. Step 2: Determine the lengths of the missing sides. The total height is 2.5 cm + 1.5 cm = 4 cm. This is the length of the leftmost vertical side. The total width is 4 cm. The top horizontal segment is 2 cm. So the inner horizontal segment is 4 cm - 2 cm = 2 cm. Step 3: Sum all side lengths to find the perimeter. P = 2 cm + 2.5 cm + 2 cm + 1.5 cm + 4 cm + 4 cm P = 16 cm The perimeter of Shape B is 16 cm. Shape C: Step 1: Identify the dimensions of the triangle. The sides are 3.8 m, 5.3 m, and 4.9 m. Step 2: Sum all side lengths to find the perimeter. P = 3.8 m + 5.3 m + 4.9 m P = 14.0 m The perimeter of Shape C is 14.0 m. Shape D: Step 1: Identify the given side lengths. Assuming it's a right-angled triangle with legs 12.4 cm and 68.2 cm. Step 2: Calculate the length of the hypotenuse using the Pythagorean theorem c = sqrt(a^2 + b^2). c = sqrt((12.4 cm))^2 + (68.2 cm)^2 c = sqrt(153.76 cm)^2 + 4651.24 cm^2 c = sqrt(4805 cm)^2 c ≈ 69.318 cm Step 3: Sum all side lengths to find the perimeter. P = 12.4 cm + 68.2 cm + 69.318 cm P ≈ 149.918 cm Rounding to two decimal places: P ≈ 149.92 cm The perimeter of Shape D is 149.92 cm. Shapes below EXERCISE 35.2 Shape A: Step 1: Identify the side lengths and convert inconsistent units. The sides are 2 m, 700 cm, 3 m, and 10 m. The measurement not in meters is 700 cm. Convert 700 cm to meters: 700 cm = 7 m. Step 2: Determine the lengths of the missing sides for the L-shape. The total width is 10 m. The top segment is 2 m. So the inner horizontal segment is 10 m - 2 m = 8 m. The total height is 7 m. The left segment is 3 m. So the inner vertical segment is 7 m - 3 m = 4 m. Step 3: Sum all side lengths to find the perimeter. P = 2 m + 7 m + 10 m + 3 m + 8 m + 4 m P = 34 m The perimeter of Shape A is 34 m. Shape B: Step 1: Identify the side lengths and convert inconsistent units. The sides are 270 cm, 3.5 m, 1.9 m, 8 cm, 2.8 m, and 2 m. The measurements not in meters are 270 cm and 8 cm. Convert 270 cm to meters: 270 cm = 2.7 m. Convert 8 cm to meters: 8 cm = 0.08 m. Step 2: Sum all side lengths to find the perimeter. P = 2.7 m + 3.5 m + 1.9 m + 0.08 m + 2.8 m + 2 m P = 12.98 m The perimeter of Shape B is 12.98 m. Shape C: Step 1: Identify the side lengths and convert inconsistent units. The sides are 3.5 cm, 4 cm, 4.5 cm, 5 cm, 12 cm, 90 mm, 3.5 cm, 4 cm. The measurement not in centimeters is 90 mm. Convert 90 mm to centimeters: 90 mm = 9 cm. Step 2: Sum all side lengths to find the perimeter. P = 9 cm + 12 cm + 9 cm + 3.5 cm + 4 cm + 4.5 cm + 5 cm + 4.5 cm + 4 cm + 3.5 cm P = 59 cm The perimeter of Shape C is 59 cm. Send me the next one 📸