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

Question

https://gmatclub.com/forum/download/file.php?id=44365 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 triangles.jpg

GMATinsight · Answer

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

AvidDreamer09 · Answer

OA is E.... does anyone know why????

GMATinsight · Answer

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

Bunuel · Answer

_________________________
The OA is B. Edited. Thank you.

Salsanousi · Answer

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

exc4libur · Answer

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?

GMATinsight · Answer

exc4libur

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

exc4libur · Answer

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?

GMATinsight · Answer

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

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.

Prep Toolkit

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