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
here's the solution for question 15: Question 15: In the figure below BC=24cm, APD = PCD = PBA = 90^. Calculate, correct to 2 decimal places, the length AD given that P is the midpoint of BC. Step 1: Determine the lengths of BP and PC. Given that P is the midpoint of BC and BC = 24 cm: BP = PC = (BC)/(2) = 24 cm2 = 12 cm Step 2: Calculate the length of AP using triangle PBA. Triangle PBA is a right-angled triangle at B ( PBA = 90^). We have AB = 5 cm and BP = 12 cm. Using the Pythagorean theorem (a^2 + b^2 = c^2): AP^2 = AB^2 + BP^2 AP^2 = (5 cm)^2 + (12 cm)^2 AP^2 = 25 cm^2 + 144 cm^2 AP^2 = 169 cm^2 AP = sqrt(169 cm)^2 = 13 cm Step 3: Calculate the length of PD using triangle PCD. Triangle PCD is a right-angled triangle at C ( PCD = 90^). We have CD = 18 cm and PC = 12 cm. Using the Pythagorean theorem: PD^2 = PC^2 + CD^2 PD^2 = (12 cm)^2 + (18 cm)^2 PD^2 = 144 cm^2 + 324 cm^2 PD^2 = 468 cm^2 PD = sqrt(468 cm)^2 Step 4: Calculate the length of AD using triangle APD. Triangle APD is a right-angled triangle at P ( APD = 90^). We have AP = 13 cm and PD = sqrt(468) cm. Using the Pythagorean theorem: AD^2 = AP^2 + PD^2 AD^2 = (13 cm)^2 + (sqrt(468 cm)^2)^2 AD^2 = 169 cm^2 + 468 cm^2 AD^2 = 637 cm^2 AD = sqrt(637 cm)^2 Step 5: Calculate the final value and round to 2 decimal places. AD ≈ 25.23885 cm Rounding to 2 decimal places: AD ≈ 25.24 cm The length AD is: 25.24 cm That's 4 down, 1 left today. Send me the next one 📸