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Which of the following must be true? (I) The area of triangle P.

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Which of the following must be true? (I) The area of triangle P.  [#permalink]

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New post Updated on: 15 Jul 2019, 04:23
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A
B
C
D
E

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Question Stats:

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Which of the following must be true?

(I) The area of triangle P.
(II) The area of triangle Q.
(III) The area of triangle R.

(A) I = II = III
(B) I < II < III
(C) I > II < III
(D) III < I < II
(E) III > I > II

Source: Nova GMAT
Difficulty Level: 700

Attachment:
triangles.jpg
triangles.jpg [ 28.56 KiB | Viewed 1001 times ]

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Originally posted by Bunuel on 09 Oct 2018, 21:52.
Last edited by SajjadAhmad on 15 Jul 2019, 04:23, edited 1 time in total.
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Re: Which of the following must be true? (I) The area of triangle P.  [#permalink]

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New post 10 Oct 2018, 02:16
1
Bunuel wrote:
Image
Which of the following must be true?

(I) The area of triangle P.
(II) The area of triangle Q.
(III) The area of triangle R.

(A) I = II = III
(B) I < II < III
(C) I > II < III
(D) III < I < II
(E) III > I > II

Attachment:
triangles.jpg


\(Area of P = (√3/4)*10^2\)
\(Area of Q = (1/2)*10^2\)

i.e. Area of Q is greater than Area of P i.e. II > I i.e. Answer must be out of choices B and D

Also from Triangle Q, \(y = √(10^2 + 5^2) = 5√5 = 11.1\)

i.e. Area of \(R = (1/2)*11.1^2\) which is even greater than Area of Q

Answer: Option B
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Re: Which of the following must be true? (I) The area of triangle P.  [#permalink]

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New post 13 Oct 2018, 23:46
OA is E.... does anyone know why????
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Re: Which of the following must be true? (I) The area of triangle P.  [#permalink]

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New post 14 Oct 2018, 01:53
Bunuel wrote:
Image
Which of the following must be true?

(I) The area of triangle P.
(II) The area of triangle Q.
(III) The area of triangle R.

(A) I = II = III
(B) I < II < III
(C) I > II < III
(D) III < I < II
(E) III > I > II

Attachment:
triangles.jpg



Bunuel
Please check answer or post explanation
I still think answer is option B
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Re: Which of the following must be true? (I) The area of triangle P.  [#permalink]

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New post 14 Oct 2018, 02:03
GMATinsight wrote:
Bunuel wrote:
Image
Which of the following must be true?

(I) The area of triangle P.
(II) The area of triangle Q.
(III) The area of triangle R.

(A) I = II = III
(B) I < II < III
(C) I > II < III
(D) III < I < II
(E) III > I > II

Attachment:
triangles.jpg



Bunuel
Please check answer or post explanation
I still think answer is option B

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The OA is B. Edited. Thank you.
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Re: Which of the following must be true? (I) The area of triangle P.  [#permalink]

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New post 14 Oct 2018, 02:44
Bunuel wrote:
Image
Which of the following must be true?

(I) The area of triangle P.
(II) The area of triangle Q.
(III) The area of triangle R.

(A) I = II = III
(B) I < II < III
(C) I > II < III
(D) III < I < II
(E) III > I > II

Attachment:
triangles.jpg


Area of triangle P = \(s^2 \sqrt{3} * \frac{1}{4}\) = \(10^2 * \sqrt{3} * \frac{1}{4} = 25\sqrt{3}\)

Area of triangle Q = \(\frac{10*10}{2} = 50\)

We can find the value of y from triangle q to be \(y^2 = 10^2 + 5^2 = 125\)

Area of triangle R = \(\frac{y^2}{2} = 125/2 = 62.5\)

III > II > I

Answer choice B
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Which of the following must be true? (I) The area of triangle P.  [#permalink]

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New post 09 Oct 2019, 06:45
Bunuel wrote:
Image
Which of the following must be true?

(I) The area of triangle P.
(II) The area of triangle Q.
(III) The area of triangle R.

(A) I = II = III
(B) I < II < III
(C) I > II < III
(D) III < I < II
(E) III > I > II


Hey GMATinsight Bunuel VeritasKarishma GMATPrepNow,

How do you know that in Q the line from the vertex perpendicular to the opposite side is the height/alt = 10, and that it bisects the opposite side?
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Re: Which of the following must be true? (I) The area of triangle P.  [#permalink]

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New post 09 Oct 2019, 06:56
exc4libur wrote:
Bunuel wrote:
Image
Which of the following must be true?

(I) The area of triangle P.
(II) The area of triangle Q.
(III) The area of triangle R.

(A) I = II = III
(B) I < II < III
(C) I > II < III
(D) III < I < II
(E) III > I > II


Hey GMATinsight Bunuel VeritasKarishma GMATPrepNow,

How do you know that in Q the line from the vertex perpendicular to the opposite side is the height/alt = 10, and that it bisects the opposite side?


exc4libur

Because it's an isosceles triangle and the perpendicular dropped from the vertex where two equal sides meet is also the bisector.
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Re: Which of the following must be true? (I) The area of triangle P.  [#permalink]

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New post 09 Oct 2019, 07:04
GMATinsight wrote:
exc4libur wrote:
Bunuel wrote:
Image
Which of the following must be true?

(I) The area of triangle P.
(II) The area of triangle Q.
(III) The area of triangle R.

(A) I = II = III
(B) I < II < III
(C) I > II < III
(D) III < I < II
(E) III > I > II


How do you know that in Q the line from the vertex perpendicular to the opposite side is the height/alt = 10, and that it bisects the opposite side?


exc4libur

Because it's an isosceles triangle and the perpendicular dropped from the vertex where two equal sides meet is also the bisector.


So I could say that: any isosceles triangle in which a perpendicular line from the vertex, where equal sides meet, to the opposite side, bisects the opposite side and is the altitude of the triangle?
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Re: Which of the following must be true? (I) The area of triangle P.  [#permalink]

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New post 09 Oct 2019, 08:02
1
exc4libur wrote:
GMATinsight wrote:
exc4libur wrote:
Image
Which of the following must be true?

(I) The area of triangle P.
(II) The area of triangle Q.
(III) The area of triangle R.

(A) I = II = III
(B) I < II < III
(C) I > II < III
(D) III < I < II
(E) III > I > II


How do you know that in Q the line from the vertex perpendicular to the opposite side is the height/alt = 10, and that it bisects the opposite side?


exc4libur

Because it's an isosceles triangle and the perpendicular dropped from the vertex where two equal sides meet is also the bisector.


So I could say that: any isosceles triangle in which a perpendicular line from the vertex, where equal sides meet, to the opposite side, bisects the opposite side and is the altitude of the triangle?
exc4libur

Yes, now you are correct
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Re: Which of the following must be true? (I) The area of triangle P.   [#permalink] 09 Oct 2019, 08:02
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