City B is 5 miles east of city A. City C is 10 miles southeast of city B. Which of the following is the closest to the distance from city A to City C?

Correct Answer: 14 miles
Here , AB = 5 miles, BC = 10 miles ∆BDC is an isosceles right  - angled triangle..'. BC2 = BD2 + CD2⇒102 = x2 + x2⇒2x2 = 100⇒x2 = 50 = 25×2⇒x = 52.'. AD = AB + BD  = 5  + 52Now, AC2 = (5 + 52)2  + (52)2 = (5 + 5×1.414)2  + 50 = 195.68⇒AC = 13.99 ≃ 14