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

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Math Expert
Joined: 02 Sep 2009
Posts: 58453
Which of the following must be true? (I) The area of triangle P.  [#permalink]

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Updated on: 15 Jul 2019, 04:23
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Difficulty:

75% (hard)

Question Stats:

65% (02:33) correct 35% (02:40) wrong based on 80 sessions

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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 [ 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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10 Oct 2018, 02:16
1
Bunuel wrote:

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

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

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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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14 Oct 2018, 01:53
Bunuel wrote:

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
I still think answer is option B
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Posts: 58453
Re: Which of the following must be true? (I) The area of triangle P.  [#permalink]

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14 Oct 2018, 02:03
GMATinsight wrote:
Bunuel wrote:

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
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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14 Oct 2018, 02:44
Bunuel wrote:

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

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

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09 Oct 2019, 06:45
Bunuel wrote:

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

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09 Oct 2019, 06:56
exc4libur wrote:
Bunuel wrote:

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

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09 Oct 2019, 07:04
GMATinsight wrote:
exc4libur wrote:
Bunuel wrote:

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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09 Oct 2019, 08:02
1
exc4libur wrote:
GMATinsight wrote:
exc4libur wrote:

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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