City B is 5miles of city A because the given condition forms a right angled triangle... City A to B is 5miles. B to C is 10miles and A to C is 11.25 miles

veerangana

Oct 9th, 2016

If C is directly below B (i.e south of B), then ABC will be a right angled triangle and AC will be the hypotenuse.
Hence the min. distance will be sqrt (125)
However, since C is south east of B... ABC is not right angled triangle... and AC should be > sqrt (125) which is 12

Mir Mahdi Hasan

Aug 5th, 2019

BC = 10
AB = 5
Now,
BC^2 = BK^2 + CK^2
10^2 = BK^2 + BK^2 [ BK = CK]
10^2 = 2BK^2
BK^2 = 5^2
BK = 5 = CK
AK = AB + BK
AK = 5 + 5
AK = 10 AC^2 = CK^2 + AK^2
AC^2 = 5^2 + 10^2
AC^2 = 25+ 100
AC = Root(125)
AC = 11.18 So That AC value is 11.18

## 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?

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