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City B is 5 miles east of the city A, city C is 10 miles

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City B is 5 miles east of the city A, city C is 10 miles [#permalink]

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02 Feb 2008, 12:22
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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
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02 Feb 2008, 12:31
Without doing any real math I'd hazard a guess of C. 13

If this happens to be correct I'll explain my "logic"
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02 Feb 2008, 12:55
C south of B would have given closest A-C distance as $$5sqrt5$$~11.15 miles. But C is south East of B, so lets move C a bit right and go for the next higher number 12

I am correcting it now.. the answer is 14

C has to be moved 45 deg away from the south

which means we have a right triangle, with base as 5+sqrt50 and height as sqrt50, the hypnoteuse we need to find.

sqrt(25+50+50+10sqrt50) = ~14
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04 Feb 2008, 13:54

1) 10 miles southeast of B means 45 a degree angle from the origin towards the 3rd quadrant.
2) The diagonal is 10, and the angle is 45, so we have an isosceles right triangle. With sides 10, 10/√2,10/√2 = 10,7,7 (approximation)
3) This makes the horizontal distance from A to C = 5+7=12
4) Vertical distance is still 7 (10/√2)
5) Poblem turns into H^2= 12^2+7^2 ------ = √(144+49)
6) 13.90 ---- = 14
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04 Feb 2008, 14:35
sqrt([sqrt(10)/2]^2 + [sqrt(10)/2+5]^2) close to 14 -> D
Re: PS:   [#permalink] 04 Feb 2008, 14:35
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