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# In the triangle above, lengths AC and BD are both equal to the same in

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Math Expert
Joined: 02 Sep 2009
Posts: 56275
In the triangle above, lengths AC and BD are both equal to the same in  [#permalink]

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24 Aug 2017, 23:35
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Difficulty:

35% (medium)

Question Stats:

73% (01:51) correct 27% (01:37) wrong based on 57 sessions

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In the triangle above, lengths AC and BD are both equal to the same integer. Which of the following could NOT be the area of ∆ ABC?

(A) 1/2
(B) 4 1/2
(C) 6
(D) 8
(E) 12 1/2

Attachment:

2017-08-24_1251_002.png [ 4.37 KiB | Viewed 932 times ]

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Re: In the triangle above, lengths AC and BD are both equal to the same in  [#permalink]

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24 Aug 2017, 23:43
1

If the integer the base and height are equal to is x,
the area for the triangle is $$\frac{1}{2}*x^2 = \frac{x^2}{2}$$

Of the answer options available (after converting the mixed fractions to proper fraction)
(A) $$\frac{1}{2}$$
(B) $$4\frac{1}{2}$$ = $$\frac{9}{2}$$
(C) $$6 = \frac{12}{2}$$
(D) $$8 = \frac{16}{2}$$
(E) $$12\frac{1}{2} = \frac{25}{2}$$

The numerator is not a square only in Option C and is our correct answer!
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Re: In the triangle above, lengths AC and BD are both equal to the same in  [#permalink]

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25 Aug 2017, 00:03
Bunuel wrote:

In the triangle above, lengths AC and BD are both equal to the same integer. Which of the following could NOT be the area of ∆ ABC?

(A) 1/2
(B) 4 1/2
(C) 6
(D) 8
(E) 12 1/2

Attachment:
2017-08-24_1251_002.png

1/2 is 1/2 * 1^2
9/2 is 1/2 * 3^2
12/2 is 1/2 * not an integer
16/2 is 1/2 * 4^2
25/2 is 1/2 * 5^2
C
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Re: In the triangle above, lengths AC and BD are both equal to the same in  [#permalink]

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27 Aug 2018, 02:34
Let AC and BD be x, then the area $$A = x^2/2$$

A*2 = x^2 
This means that $$A*2$$ has to be a perfect square. Of the answer choices only $$6*2 = 12$$ is not a perfect square.

Re: In the triangle above, lengths AC and BD are both equal to the same in   [#permalink] 27 Aug 2018, 02:34
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