rishi2377 wrote:

1. City B is 5 miles east of the 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?

A. 11 miles

B. 12 miles

C. 13 miles

D. 14 miles

E. 15 miles

lets drop a line from c to the base and called it k.

AC^2 = BK^2 + CK^2

10^2 = 2 BK^2 (since BK=CK)

BK = 10/sqrt = 5 sqrt2

CK = 5 sqrt2

AK = AB+BK = 5 + 5 sqrt2

AC = sqrt [CK^2 + AK^2)

AC = sqrt [(5+5 sqrt2)^2 +

(5 sqrt2)^2]

AC = sqrt [25+ 2x5x5 sqrt2 + 50]

AC = sqrt [75 + 50 sqrt2]

AC = sqrt [75 + 50 x 1.41]

AC = sqrt [75 + 71]

AC = sqrt [146]

AC = approx 12

i missed to include the red part above.