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.
ScanSolve AI Answer
Step 1: Determine the type of triangle. We are given the side lengths PQ = 8 cm, PR = 6 cm, and QR = 10 cm. We check if it's a right-angled triangle using the Pythagorean theorem (a^2 + b^2 = c^2). PQ^2 + PR^2 = 8^2 + 6^2 = 64 + 36 = 100 QR^2 = 10^2 = 100 Since PQ^2 + PR^2 = QR^2, the triangle PQR is a right-angled triangle with the right angle at P. For angle x at vertex Q: • The side opposite to x is PR = 6 cm. • The side adjacent to x is PQ = 8 cm. • The hypotenuse is QR = 10 cm. Step 2: Calculate x, x, and x. Using SOH CAH TOA: x = OppositeHypotenuse = (PR)/(QR) = (6)/(10) = (3)/(5) x = AdjacentHypotenuse = (PQ)/(QR) = (8)/(10) = (4)/(5) x = OppositeAdjacent = (PR)/(PQ) = (6)/(8) = (3)/(4) So, for part i): x = (3)/(5), x = (4)/(5), x = (3)/(4) Step 3: Calculate x - x. Substitute the values found in Step 2: x - x = (3)/(5) - (4)/(5) = (3-4)/(5) = -(1)/(5) So, for part ii): x - x = -(1)/(5) Step 4: Calculate ( x + x)^2. Substitute the values found in Step 2: x + x = (3)/(5) + (3)/(4) Find a common denominator, which is 20: (3)/(5) + (3)/(4) = (3 × 4)/(5 × 4) + (3 × 5)/(4 × 5) = (12)/(20) + (15)/(20) = (12+15)/(20) = (27)/(20) Now, square the result: ((27)/(20))^2 = (27^2)/(20^2) = (729)/(400) So, for part iii): ( x + x)^2 = (729)/(400) Send me the next one 📸