What is the length of the shortest path from A to D?

Question

Segment BC perpendicular to Segment CD

Segment BC perpendicular to Segment AB

AB=3

BC=6

CD=5

A.) 14

B.) 12

C.) 10√2

D.) 10

Answer 1

Draw it out. CD is base with length 5. BC is altitude with length 6. AB is at top of altitude and parallel to CD. The smallest distance is when AB is such that A is closer to D (In an almost C shape). The distance from A to D is now 6 up and (5-3) across. The smallest distance for AD is sqrt(6²+2²) = sqrt(40) = 2sqrt(10) Not one of the answers. Longest path is 10.

Please consider a tutor. Take care.