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 for Question 3 and Question 4: QUESTION 3: MEASUREMENT 3.1 Step 1: Identify the formula for the perimeter of a rectangle. The perimeter P of a rectangle is given by P = 2 × (length + width). Step 2: Substitute the given values. Length = 22 m, Width = 2 m. P = 2 × (22 m + 2 m) P = 2 × (24 m) P = 48 m The perimeter of the bridge walkway is 48 m. 3.2 Step 1: Identify the formula for the area of a rectangle. The area A of a rectangle is given by A = length × width. Step 2: Substitute the given values. Length = 22 m, Width = 2 m. A = 22 m × 2 m A = 44 m^2 The area of the walkway is 44 m^2. 3.3 Step 1: Identify the relevant theorem for a right-angled triangle. The Pythagorean theorem states that a^2 + b^2 = c^2, where a and b are the lengths of the two shorter sides (legs) and c is the length of the hypotenuse (the cable). Step 2: Substitute the given values. Vertical post (a) = 3 m, Horizontal distance (b) = 4 m. 3^2 + 4^2 = c^2 9 + 16 = c^2 25 = c^2 Step 3: Solve for c. c = sqrt(25) c = 5 m The length of the cable is 5 m. 3.4 Step 1: Recall the conversion factor between meters and centimeters. 1 m = 100 cm. Step 2: Convert the length of the bridge walkway from meters to centimeters. Length = 22 m. 22 m × 100 cmm = 2200 cm The length of the bridge walkway in centimeters is 2200 cm. 3.5 I cannot draw the sketch for you, but here's how you should approach it: Step 1: Determine the dimensions for the sketch using the given scale. The scale is 2 cm : 200 cm, which simplifies to 1 cm : 100 cm (or 1 cm : 1 m). Original length = 22 m = 2200 cm. Scaled length = 2200 cm × 1 cm100 cm = 22 cm. Original width = 2 m = 200 cm. Scaled width = 200 cm × 1 cm100 cm = 2 cm. Step 2: Draw a rectangle with the scaled dimensions. Draw a rectangle that is 22 cm long and 2 cm wide. Label its vertices as P, Q, R, S. QUESTION 4: SPACE AND SHAPE 4.1 If a triangle has two equal angles, it must also have two equal sides. A triangle with two equal sides is classified as an isosceles triangle. The triangle is an isosceles triangle. 4.2 Step 1: Recall the sum of angles in a triangle. The sum of the interior angles in any triangle is 180^. Step 2: Calculate the third angle. Given two angles are 70^ each. Third angle = 180^ - (70^ + 70^) Third angle = 180^ - 140^ Third angle = 40^ The size of the third angle is 40^. 4.3 When a triangle is translated (moved without rotation or reflection), its shape and size remain unchanged. Other properties that remain unchanged include its side lengths, angle measures, area, and perimeter. Two properties that remain unchanged are: • The side lengths of the triangle. • The angle measures of the triangle. 4.4 To ensure that the triangular braces have equal angles, you would make all three angles equal to 60^. This would result in an equilateral triangle, where all angles and all sides are equal. You would make all three angles equal to 60^. That's 2 down. 3 left today — send the next one.