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On a map Town G is 10 centimeters due east of Town H and 8 centimeters

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On a map Town G is 10 centimeters due east of Town H and 8 centimeters [#permalink]

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New post 28 Aug 2017, 02:18
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On a map Town G is 10 centimeters due east of Town H and 8 centimeters due south of Town J. Which of the following is closest to the straight-line distance, in centimeters, between Town H and Town J on the map?

A. 6
B. 13
C. 18
D. 20
E. 24
[Reveal] Spoiler: OA

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Re: On a map Town G is 10 centimeters due east of Town H and 8 centimeters [#permalink]

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New post 28 Aug 2017, 02:35
Answer is 13 as √164 is closest to 13
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Re: On a map Town G is 10 centimeters due east of Town H and 8 centimeters [#permalink]

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New post 28 Aug 2017, 02:58
Bunuel wrote:
On a map Town G is 10 centimeters due east of Town H and 8 centimeters due south of Town J. Which of the following is closest to the straight-line distance, in centimeters, between Town H and Town J on the map?

A. 6
B. 13
C. 18
D. 20
E. 24


- We can create a right triangle with legs = 10 cm and 8 cm.
- Question asked about closest straight line distance - the same as the hypotenuse of triangle JGH.
- Hypotenuse = \(\sqrt{10^2+8^2} = \sqrt{164}\)
- Approximately, it is closer to 13 (\(13^2 = 169\), 5 more than 164).

B.
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Re: On a map Town G is 10 centimeters due east of Town H and 8 centimeters [#permalink]

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New post 29 Aug 2017, 00:25
Bunuel wrote:
On a map Town G is 10 centimeters due east of Town H and 8 centimeters due south of Town J. Which of the following is closest to the straight-line distance, in centimeters, between Town H and Town J on the map?

A. 6
B. 13
C. 18
D. 20
E. 24


Answer is B. It forms the right angle triangle and we just need to find hypotenuse of it. Which is 164^1/2. This is close to 169^1/2 which is equal to 13

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Re: On a map Town G is 10 centimeters due east of Town H and 8 centimeters [#permalink]

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New post 31 Aug 2017, 10:21
Bunuel wrote:
On a map Town G is 10 centimeters due east of Town H and 8 centimeters due south of Town J. Which of the following is closest to the straight-line distance, in centimeters, between Town H and Town J on the map?

A. 6
B. 13
C. 18
D. 20
E. 24


Using the information in the stem, we see that the distance between Town H and Town J is the hypotenuse of a right triangle with legs of 8 and 10. Thus:

8^2 + 10^2 = x^2

164 = x^2

√164 = √x^2

√164 = x

Since 164 is close to 169, √164 ≈ √169 = 13.

Answer: B
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Re: On a map Town G is 10 centimeters due east of Town H and 8 centimeters   [#permalink] 31 Aug 2017, 10:21
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