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27 Aug 2015, 01:38
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A
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
95%
(hard)
Question Stats:
42% (02:29) correct
58%
(02:50)
wrong
based on 172
sessions
History
Date
Time
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Not Attempted Yet
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.
(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.
27 Aug 2015, 05:47
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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
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
General Discussion
28 Aug 2015, 18:50
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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
hence answer is A
1. gives value of the area; sufficient
2. area of triangle value is not certain;insufficient
hence answer is A
