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# Triangle RST lies in the xy-plane. Point R has coordinates (a,b), poin

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Math Expert
Joined: 02 Sep 2009
Posts: 44288
Triangle RST lies in the xy-plane. Point R has coordinates (a,b), poin [#permalink]

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27 Aug 2015, 01:38
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85% (hard)

Question Stats:

47% (02:03) correct 53% (02:50) wrong based on 90 sessions

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Triangle RST lies in the xy-plane. Point R has coordinates (a,b), point S is at the origin, and point T has coordinates (c,d), such that bd + ac = 0. What is the area of triangle RST?

(1) $$(\sqrt{a^2+b^2}) (\sqrt{c^2+d^2})=48$$

(2) $$\sqrt{a^2+b^2} + \sqrt{c^2+d^2}=14$$

Kudos for a correct solution.
[Reveal] Spoiler: OA

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Joined: 14 Mar 2014
Posts: 148
GMAT 1: 710 Q50 V34
Re: Triangle RST lies in the xy-plane. Point R has coordinates (a,b), poin [#permalink]

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27 Aug 2015, 05:47
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KUDOS
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IMO : A

S(0,0) R(a,b) T(c,d)
bd+ac=0
bd = -ac
=> $$(\frac{b}{a}) * (\frac{d}{c})$$ = -1

Slope of Line SR = $$(\frac{b}{a})$$
Slope of Line ST = $$(\frac{d}{c})$$
Thus from this we can conclude that SR is Perpendicular to ST
And triangle is Right Triangle with ∠S= 90

Area of Triangle = 1/2 * SR* ST
= 1/2 * $$(\sqrt{a^2+b^2}) * (\sqrt{c^2+d^2})$$

St 1: The value is given as 48
Hence Suff

St 2 :
We can't determine unique solution.
Hence not suff
_________________

I'm happy, if I make math for you slightly clearer
And yes, I like kudos
¯\_(ツ)_/¯

Manager
Joined: 26 Dec 2012
Posts: 148
Location: United States
Concentration: Technology, Social Entrepreneurship
WE: Information Technology (Computer Software)
Re: Triangle RST lies in the xy-plane. Point R has coordinates (a,b), poin [#permalink]

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28 Aug 2015, 18:50
1
KUDOS
s be the origin and bd+ac=0; so we can say that R would be on y axis with x coordinate 0 and y coordinate as b and T can be +ve or -ve side of x axis with same x coordinate value as +or -c and y coordinate as 0. So it is an right angle triangle. area of the triangle would be 1/2 * (root a^2+b^2)*(root c^2+d^2)
1. gives value of the area; sufficient
2. area of triangle value is not certain;insufficient

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Joined: 19 Aug 2016
Posts: 73
Re: Triangle RST lies in the xy-plane. Point R has coordinates (a,b), poin [#permalink]

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12 Oct 2017, 18:53
VenoMfTw wrote:
IMO : A

S(0,0) R(a,b) T(c,d)
bd+ac=0
bd = -ac
=> $$(\frac{b}{a}) * (\frac{d}{c})$$ = -1

Slope of Line SR = $$(\frac{b}{a})$$
Slope of Line ST = $$(\frac{d}{c})$$
Thus from this we can conclude that SR is Perpendicular to ST
And triangle is Right Triangle with ∠S= 90

Area of Triangle = 1/2 * SR* ST
= 1/2 * $$(\sqrt{a^2+b^2}) * (\sqrt{c^2+d^2})$$

St 1: The value is given as 48
Hence Suff

St 2 :
We can't determine unique solution.
Hence not suff

Pls can u draw a picture to explain this?
Re: Triangle RST lies in the xy-plane. Point R has coordinates (a,b), poin   [#permalink] 12 Oct 2017, 18:53
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