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 Ismail — missed you this week. Here are the calculations for the lengths: a) Length of c Step 1: Identify the right-angled triangle. Length c is the hypotenuse of the right-angled triangle VYX. Step 2: Determine the lengths of the sides. The side VY = 4 cm. The side VX = 6 cm (given as the height of the rectangle). Step 3: Apply the Pythagorean theorem. c^2 = VY^2 + VX^2 c^2 = 4^2 + 6^2 c^2 = 16 + 36 c^2 = 52 Step 4: Calculate c and round to one decimal place. c = sqrt(52) ≈ 7.211 c ≈ 7.2 cm b) Length of a Step 1: Identify the right-angled triangle. Length a is the hypotenuse of the right-angled triangle UZY. Step 2: Determine the lengths of the sides. The side UZ = 2 cm. The side UY = UV - VY = 10 cm - 4 cm = 6 cm. Step 3: Apply the Pythagorean theorem. a^2 = UZ^2 + UY^2 a^2 = 2^2 + 6^2 a^2 = 4 + 36 a^2 = 40 Step 4: Calculate a and round to one decimal place. a = sqrt(40) ≈ 6.325 a ≈ 6.3 cm c) Length of b Step 1: Identify the right-angled triangle. Length b is the hypotenuse of the right-angled triangle ZWX. Step 2: Determine the lengths of the sides. The side WX = 10 cm. The side ZW = UW - UZ = 6 cm - 2 cm = 4 cm. Step 3: Apply the Pythagorean theorem. b^2 = ZW^2 + WX^2 b^2 = 4^2 + 10^2 b^2 = 16 + 100 b^2 = 116 Step 4: Calculate b and round to one decimal place. b = sqrt(116) ≈ 10.770 b ≈ 10.8 cm Send me the next one 📸