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
You're on a roll — Step 1: Identify the relevant triangle and the theorem. The problem asks for the length of AD. The diagram shows a right angle at point B, which means that ABD is a right-angled triangle. The sides AB and BD are the legs, and AD is the hypotenuse. We will use the Pythagorean theorem: AD^2 = AB^2 + BD^2 Step 2: Identify the lengths of the legs of ABD. From the diagram: • The length of leg AB = 9 cm. • The length of leg BD is the sum of BC and CD. BD = BC + CD Given BC = 18 cm and CD = 120 cm. Note on inconsistency: The diagram also shows AC = 17 m. However, if ABC is a right-angled triangle at B with AB=9 cm and BC=18 cm, then AC should be sqrt(9^2 + 18^2) = sqrt(81 + 324) = sqrt(405) ≈ 20.12 cm. The given AC = 17 m = 1700 cm is inconsistent with these values and the right angle at B. Since AC is not needed to find AD using ABD, we will proceed by ignoring the value of AC. Step 3: Calculate the length of BD. BD = 18 cm + 120 cm BD = 138 cm Step 4: Substitute the lengths of AB and BD into the Pythagorean theorem. AD^2 = (9 cm)^2 + (138 cm)^2 Step 5: Calculate the squares of the side lengths. AD^2 = 81 cm^2 + 19044 cm^2 Step 6: Add the squared values. AD^2 = 19125 cm^2 Step 7: Solve for AD by taking the square root. AD = sqrt(19125 cm)^2