The diagram shows two angles on a straight line. a) Find the value of a. b) Find the perimeter of the following triangle. c) The area of this trapezium is 6000 cm², find the second parallel length.

Step 1: Set up the equation for angles on a straight line. Angles on a straight line sum to 180^. (3a + 10)^ + (4a - 30)^ = 180^ Step 2: Combine like terms. 3a + 4a + 10 - 30 = 180 7a - 20 = 180 Step 3: Isolate the term with a. 7a = 180 + 20 7a = 200 Step 4: Solve for a. a = (200)/(7) The value of a is (200)/(7). b) Find the perimeter of the following triangle. Step 1: Identify the properties of the triangle. The triangle is isosceles, with a base of 16 cm and a height of 6 cm. The height bisects the base, forming two right-angled triangles. Step 2: Calculate the base of one right-angled triangle. The base of each right-angled triangle is 16 cm2 = 8 cm. Step 3: Use the Pythagorean theorem to find the length of the equal sides. Let s be the length of the equal sides. s^2 = (8 cm)^2 + (6 cm)^2 s^2 = 64 cm^2 + 36 cm^2 s^2 = 100 cm^2 s = sqrt(100 cm)^2 s = 10 cm Step 4: Calculate the perimeter of the triangle. Perimeter = base + side + side Perimeter = 16 cm + 10 cm + 10 cm Perimeter = 36 cm The perimeter of the triangle is 36 cm. c) The area of this trapezium is 6000 cm^2, find the second parallel length. Step 1: Identify the given values for the trapezium. Area (A) = 6000 cm^2 One parallel length (b_1) = 90 cm Height (h) = 160 cm Let the second parallel length be b_2. Step 2: Write the formula for the area of a trapezium. A = (1)/(2) (b_1 + b_2) h Step 3: Substitute the known values into the formula. 6000 cm^2 = (1)/(2) (90 cm + b_2) (160 cm) Step 4: Simplify the equation. 6000 = (90 + b_2) (160)/(2) 6000 = (90 + b_2) 80 Step 5: Isolate the term with b_2. (6000)/(80) = 90 + b_2 75 = 90 + b_2 Step 6: Solve for b_2. b_2 = 75 - 90 b_2 = -15 cm The calculated second parallel length is -15 cm. Note: A physical length cannot be negative. This indicates a potential inconsistency in the problem's given values. Send me the next one 📸