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

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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

Bunuel
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]
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

_________________________
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

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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

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]
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]
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]
1
Kudos
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
Re: Which of the following must be true? (I) The area of triangle P. [#permalink]
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