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# In triangle FGH, FH = 126.3 and the altitude from G is x. Which of the

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In triangle FGH, FH = 126.3 and the altitude from G is x. Which of the  [#permalink]

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23 Jun 2020, 05:16
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In triangle FGH, FH = 126.3 and the altitude from G is x. Which of the following could be the value of x if the area of the triangle is an integer?

I. 40
II. 80
III. 150

A. I only
B. II only
C. I and II only
D. II and III only
E. I, II, and III

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1.png [ 13.41 KiB | Viewed 306 times ]

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Re: In triangle FGH, FH = 126.3 and the altitude from G is x. Which of the  [#permalink]

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23 Jun 2020, 05:26
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Bunuel I think in the line, FH = 126.3 and FH = h where H value is asked. When its already given, there is some misinterpretation. Kindly confirm.

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Re: In triangle FGH, FH = 126.3 and the altitude from G is x. Which of the  [#permalink]

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23 Jun 2020, 05:31
yashikaaggarwal wrote:
Bunuel I think in the line, FH = 126.3 and FH = h where H value is asked. When its already given, there is some misinterpretation. Kindly confirm.

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Re: In triangle FGH, FH = 126.3 and the altitude from G is x. Which of the  [#permalink]

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23 Jun 2020, 05:51
The answer should be b*h/2 yields an integer. 126.3 will be 126+0.3. 126* any of the answers yields an integer, so check the 0.3
80/2 is 40 40*0.3 yields an integer
40/2 is 20 20*0.3 is an integer
150/2 is 75. 75*0.3 is not

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In triangle FGH, FH = 126.3 and the altitude from G is x. Which of the  [#permalink]

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23 Jun 2020, 06:12
Bunuel wrote:

In triangle FGH, FH = 126.3 and the altitude from G is x. Which of the following could be the value of x if the area of the triangle is an integer?

I. 40
II. 80
III. 150

A. I only
B. II only
C. I and II only
D. II and III only
E. I, II, and III

Attachment:
1.png

$$Area = (\frac{1}{2})Base*Height$$

Base = 126.3 = 1263/10

i..e. $$Area = (\frac{1}{2})*(\frac{1263}{10})*x$$

i.e. x must be a multiple of 20 for Area to be an Integer

I. 40 GOOD
II. 80 GOOD
III. 150 NOT a multiple of 20

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In triangle FGH, FH = 126.3 and the altitude from G is x. Which of the   [#permalink] 23 Jun 2020, 06:12