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What is the ratio of area of triangle BOC to area of triangle AOC ,

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What is the ratio of area of triangle BOC to area of triangle AOC , [#permalink]

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New post Updated on: 17 Dec 2017, 05:17
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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

[Reveal] Spoiler:
Attachment:
new Q.png
new Q.png [ 7.26 KiB | Viewed 605 times ]
[Reveal] Spoiler: OA

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Originally posted by chetan2u on 17 Dec 2017, 04:15.
Last edited by Bunuel on 17 Dec 2017, 05:17, edited 1 time in total.
Edited the question.
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Re: What is the ratio of area of triangle BOC to area of triangle AOC , [#permalink]

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New post 17 Dec 2017, 04:36
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
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Re: What is the ratio of area of triangle BOC to area of triangle AOC , [#permalink]

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New post 17 Dec 2017, 11:18
chetan2u wrote:
Image
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

[Reveal] Spoiler:
Attachment:
new Q.png


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.
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Re: What is the ratio of area of triangle BOC to area of triangle AOC , [#permalink]

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New post 17 Dec 2017, 22:04
chetan2u wrote:
Image
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

[Reveal] Spoiler:
Attachment:
new Q.png


Area of a triangle = 1/2 * base * height. For both the triangles, we can see that the base is the same. But for triangle BOC, height = b, and for triangle AOC, height = a

Thus area of triangle BOC = 1/2 * base * b
Area of triangle AOC = 1/2 * base * a , so the ratio of their areas = b/a. We need to get the value of b/a

(1) a=2b . this will give us the ratio b/a, hence Sufficient.

(2) X=4, a=2. We have the value of a, but this will not give us the value of b. So Insufficient.

Hence A answer
Re: What is the ratio of area of triangle BOC to area of triangle AOC ,   [#permalink] 17 Dec 2017, 22:04
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