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A
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Difficulty:
25%
(medium)
Question Stats:
76% (01:29) correct
24%
(02:04)
wrong
based on 88
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What is the ratio of area of triangle BOC to area of triangle AOC , if the coordinates of vertices is as given in the attached figure?
(1) a = 2b
(2) X = 4 and a = 2
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17 Dec 2017, 04:36
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Area of triangle OAC = 0.5*(OA*OC)= 0.5(a*x)
Area of triangle OBC = 0.5*(OB*OC) = 0.5 (b*x)
Ratio of (Area of triangle OAC/Area of triangle OBC) = a/b
Statement 1: a= 2b ; a/b = 2 , sufficient.
Statement 2: as NO information of b is given, Not sufficient.
Answer A
Area of triangle OBC = 0.5*(OB*OC) = 0.5 (b*x)
Ratio of (Area of triangle OAC/Area of triangle OBC) = a/b
Statement 1: a= 2b ; a/b = 2 , sufficient.
Statement 2: as NO information of b is given, Not sufficient.
Answer A
17 Dec 2017, 11:18
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chetan2u
Question: find the ratio of \(\frac{Area.BOC}{Area.AOC}\)
Area of a triangle: \(\frac{base.height}{2}\)
Distance between a point and the origin: \(\sqrt{x^2+y^2}\)
Triangle BOC: \(Base=\sqrt{(0^2+b^2)}=b\), \(Height=\sqrt{(X^2+0^2)}=x\) and \(Area=\frac{b*X}{2}\)
Triangle AOC: \(Base=\sqrt{(0^2+a^2)}=a\), \(Height=\sqrt{(X^2+0^2)}=x\) and \(Area=\frac{a*X}{2}\)
Ratio of triangle areas: \(\frac{b*X}{2}*\frac{2}{a*X}=\frac{b}{a}\), so we need to find the values of \(a\) and \(b\).
(1) a = 2b. Replace \(a\) and ratio is: \(\frac{b}{a}=\frac{b}{(2b)}=\frac{1}{2}\), sufficient.
(2) X = 4 and a = 2. This only provides the value of \(a\) and nothing of \(b\), so insufficient.
(A) is the answer.
