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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Question 3.3: In rectangle ABCD, AB = 3x and BC = 4x. Find the length of AC and BD in terms of x. Step 1: Identify the properties of a rectangle. In a rectangle, all angles are 90^. Therefore, ABC is a right-angled triangle with the right angle at B. The diagonals of a rectangle are also equal in length, so AC = BD. Step 2: Use the Pythagorean theorem to find the length of diagonal AC. In ABC: AC^2 = AB^2 + BC^2 Substitute the given values AB = 3x and BC = 4x: AC^2 = (3x)^2 + (4x)^2 AC^2 = 9x^2 + 16x^2 AC^2 = 25x^2 Take the square root of both sides: AC = sqrt(25x^2) AC = 5x Step 3: Determine the length of diagonal BD. Since the diagonals of a rectangle are equal in length: BD = AC BD = 5x The length of AC is 5x and the length of BD is 5x. Send me the next one 📸