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What is the area of the trapezoid if PQ is parallel to RS, RS > PQ, th
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17 Sep 2019, 22:05
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Competition Mode Question What is the area of the trapezoid if PQ is parallel to RS, RS > PQ, the distance between the two parallel lines is 15, and the distance from R to the perpendicular drawn from P to RS is 10? (1) \(PR =\sqrt{325}\) (2) \(QS =\sqrt{325}\) Attachment:
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Re: What is the area of the trapezoid if PQ is parallel to RS, RS > PQ, th
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17 Sep 2019, 22:43
What is the area of the trapezoid if PQ is parallel to RS, RS > PQ, the distance between the two parallel lines is 15, and the distance from R to the perpendicular drawn from P to RS is 10?
STATEMENT (1)PR=\(\sqrt{325}\)
this statement gives no new information about the trapezoid we can derive it from the question prompt still, we don't know anything about QS (trapezoid can be scalene , isosceles we don't know) so we cant find RS
area of trapezoid = \(\frac{(PQ+RS)*15}{2}\)
we don't know anything about RS so, we can't find the area of a trapezoid INSUFFICIENT
STATEMENT (2)QS=\(\sqrt{325}\)
we know that PR = \(\sqrt{325}\) from this statement we know QS = \(\sqrt{325}\) this proves that trapezoid is isoceles
so we can find the value of RS that is = 10+30+10 = 50
area of trapezoid = \(\frac{(PQ+RS)*15}{2}\) = \(\frac{(30+50)*15}{2}\) = 600
SUFFICIENT
B is the correct answer



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Re: What is the area of the trapezoid if PQ is parallel to RS, RS > PQ, th
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17 Sep 2019, 22:49
IMO ANSWER IS OPTION B. Here's how I did: Posted from my mobile device
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Re: What is the area of the trapezoid if PQ is parallel to RS, RS > PQ, th
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17 Sep 2019, 23:10
From the information given in connection with the trapezoid, I need information on QS in order to compute the area of trapezoid.
1. Statement 1 gives the distance of PR=325^0.5, an information that can already be deduced from the question stem. In addition it gives no information whatsoever about QS, which is needed in order to determine the length of RS. Statement 1 is therefore insufficient.
2. Statement gives information about the QS=325^0.5, and that is sufficient to compute the area of the trapezoid. Statement 2 alone is therefore sufficient in this case.
The answer is therefore B.



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Re: What is the area of the trapezoid if PQ is parallel to RS, RS > PQ, th
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17 Sep 2019, 23:29
As we know Area of trapezoid = (a+b)h HERE a=30,h=15, to find b we need RS length= 10+15+X(CAN BE FIND USING QS) So OA:B



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Re: What is the area of the trapezoid if PQ is parallel to RS, RS > PQ, th
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17 Sep 2019, 23:40
B.
We need B to locate point S. A is already Stated in the argument
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Re: What is the area of the trapezoid if PQ is parallel to RS, RS > PQ, th
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18 Sep 2019, 00:25
Given here PQ = 30, Let T be the point at RS such that PT ⊥ RS. Given PT = 15 and RT = 10. Since RS > PQ RS > 30 Area of Trapezoid PQSR \(=\frac{1}{2} (PQ + RS) * PT\) Only unknown in the formula is RS. So RS = ? (1) PR = √325 It only reiterates what is mentioned in the question. No new information given about RS neither can be deduced. Since QS can have following possibilities: a. QS < PR b. QS = PR c. QS > PR RS would vary accordingly. INSUFFICIENT. (2) QS = √325 Since RT = 10 and PT = 15, PR = √325. Hence PR = QS RS = 10 + 30 + 10 = 50 Thus, only one value of RS is possible. SUFFICIENT. Answer(B).
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Re: What is the area of the trapezoid if PQ is parallel to RS, RS > PQ, th
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18 Sep 2019, 03:20
Quote: What is the area of the trapezoid if PQ is parallel to RS, RS > PQ, the distance between the two parallel lines is 15, and the distance from R to the perpendicular drawn from P to RS is 10?
(1) PR=√325 (2) QS=√325 area trapezoid: \(\frac{base_1+base_2}{2}•height=\frac{31+(10+30+X)}{2}•15\) X is the distance from S to the perpendicular drawn from Q to RS; (1) PR=√325: no info about perpendicular, insufic. (2) QS=√325: if we draw a right triangle from this perpendicular we can find X with this info, sufic. Answer (B)



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Re: What is the area of the trapezoid if PQ is parallel to RS, RS > PQ, th
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18 Sep 2019, 10:37
B Area = (B1+B2) * h /2 = 30*x*15/2 st1 useless st2 we can calculate the length of the base of the second " triangle " which is 10 like the one of the first triangle. Therefore the middle part is also equal to 30 so x = 10+30+10 = 50 > Sufficient
B




Re: What is the area of the trapezoid if PQ is parallel to RS, RS > PQ, th
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18 Sep 2019, 10:37






