A is 10 miles west of B. C is 30 miles north of B. D is 20 miles east of C. What is the distance from A to D ?

A. 10 miles

B. 30 miles

C. $$10\sqrt {10} $$  miles

D. $$10\sqrt {13} $$  miles

E. $$30\sqrt {2} $$  miles

Answer: Option E

Solution(By Examveda Team)

$$\eqalign{ & {\text{Required distance :}} \cr & AD = \sqrt {{{\left( {AE} \right)}^2} + {{\left( {DE} \right)}^2}} \cr & = \sqrt {{{\left( {30} \right)}^2} + {{\left( {30} \right)}^2}} \cr & = \sqrt {900 + 900} \cr & = \sqrt {1800} \cr & = 30\sqrt 2 {\text{ miles}} \cr} $$