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# Which of the following must be true?

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Which of the following must be true? [#permalink]  01 Oct 2018, 13:39
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Question Stats:

80% (01:34) correct 20% (03:38) wrong based on 20 sessions
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#GREpracticequestin Which of the following must be true.jpg [ 28.56 KiB | Viewed 2492 times ]

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
[Reveal] Spoiler: OA

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Intern
Joined: 15 Sep 2018
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Re: Which of the following must be true? [#permalink]  09 Sep 2019, 22:47
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Triangle P is an equilateral triangle, therefore, the area is (3)^(1/2) * a^(2) / 4. Which equals 25 * 3^(1/2). Approx 42.5

Triangle Q has an area of (1/2) * 10 * 10 = 50.

Also, we can determine the value of y from triangle Q. The triangle is an isosceles triangle, therefore the height must bisect the base. Using (5)^2 + (10)^2 = y^2, we get y = (125)^(1/2).

Triangle R has an area of 1/2 * y * y = 125/2 = 62.5

Therefore, P < Q < R => I < II < III.
Re: Which of the following must be true?   [#permalink] 09 Sep 2019, 22:47
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