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
Welcome back — been a while! Let's pick up where you left off. The problem provides the width and length of a rectangle in terms of r, and its perimeter. We need to find the values of the width and length. Given: Width (w) = r Length (l) = 1.7320r Perimeter (P) = 14 + 10.3923 Step 1: Calculate the total perimeter. First, sum the given parts of the perimeter. P = 14 + 10.3923 P = 24.3923 Step 2: Write the formula for the perimeter of a rectangle. The formula for the perimeter of a rectangle is P = 2(l + w). Step 3: Substitute the given expressions for length and width into the perimeter formula. Substitute l = 1.7320r and w = r into the perimeter formula, and set it equal to the calculated perimeter. 24.3923 = 2(1.7320r + r) Step 4: Solve the equation for r. Combine the terms inside the parenthesis and then solve for r. 24.3923 = 2(2.7320r) 24.3923 = 5.4640r r = (24.3923)/(5.4640) r ≈ 4.4642 Step 5: Calculate the length and width. Now substitute the value of r back into the expressions for length and width. Width: w = r w = 4.4642 Length: l = 1.7320r l = 1.7320 × 4.4642 l ≈ 7.7320 The width of the rectangle is approximately 4.4642 units and the length is approximately 7.7320 units. The width is 4.4642 and the length is 7.7320. Send me the next one 📸