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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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Updated on: 17 Dec 2017, 05:17
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Difficulty:

35% (medium)

Question Stats:

72% (01:00) correct 28% (01:34) wrong based on 57 sessions

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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

Attachment:

new Q.png [ 7.26 KiB | Viewed 720 times ]

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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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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.

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

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17 Dec 2017, 11:18
chetan2u wrote:

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

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.

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

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17 Dec 2017, 22:04
chetan2u wrote:

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

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.

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