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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Welcome back TEBZA — been a while! Let's pick up where you left off. Here's the solution for question 8: The image shows a right-angled triangle with two sides given as 8 cm and 15 cm. The side labeled 'x' is the hypotenuse. a) Calculate the length of the third side. Step 1: Identify the known sides and the unknown side. In 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 longest side, opposite the right angle). Here, the legs are 8 cm and 15 cm, and the hypotenuse is x. Step 2: Apply the Pythagorean theorem. x^2 = (8 cm)^2 + (15 cm)^2 Step 3: Calculate the squares and sum them. x^2 = 64 cm^2 + 225 cm^2 x^2 = 289 cm^2 Step 4: Find the square root to solve for x. x = sqrt(289 cm)^2 x = 17 cm The length of the third side is 17 cm. b) Determine the perimeter of the triangle. Step 1: Recall the formula for the perimeter of a triangle. The perimeter is the sum of the lengths of all three sides. Perimeter = side_1 + side_2 + side_3 Step 2: Substitute the side lengths and calculate. Perimeter = 8 cm + 15 cm + 17 cm Perimeter = 40 cm The perimeter of the triangle is 40 cm. c) Calculate the area of the triangle. Step 1: Recall the formula for the area of a right-angled triangle. Area = (1)/(2) × base × height In a right-angled triangle, the two legs can be considered the base and height. Step 2: Substitute the base and height values and calculate. Area = (1)/(2) × 8 cm × 15 cm Area = 4 cm × 15 cm Area = 60 cm^2 The area of the triangle is 60 cm^2. Send me the next one 📸