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

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Joined: 02 Sep 2009
Posts: 58409
On a map Town G is 10 centimeters due east of Town H and 8 centimeters  [#permalink]

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28 Aug 2017, 02:18
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25% (medium)

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80% (01:15) correct 20% (01:22) wrong based on 101 sessions

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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

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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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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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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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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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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.

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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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03 Apr 2018, 03:59
Fedemaravilla 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

Check the diagram below:

$$x=\sqrt{10^2+8^2}=\sqrt{164}$$, which is little less than 13^2 = 169.

Attachment:

Untitled.png [ 2.15 KiB | Viewed 1197 times ]

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

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03 Sep 2019, 06:18
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Re: On a map Town G is 10 centimeters due east of Town H and 8   [#permalink] 03 Sep 2019, 06:18
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