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

_________________________
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]
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

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


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]
Expert Reply
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


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]
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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Expert Reply
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]
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