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Math Expert V
Joined: 02 Sep 2009
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Triangles ABC and DEF are similar. What percent of the area of triangl  [#permalink]

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Question Stats: 73% (00:58) correct 27% (01:25) wrong based on 188 sessions

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Triangles ABC and DEF are similar. What percent of the area of triangle DEF is triangle ABC?

(1) Sides AB and DE connect similar angles, and AB is 3 times DE.
(2) Side AB = 9

Kudos for a correct solution.

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Re: Triangles ABC and DEF are similar. What percent of the area of triangl  [#permalink]

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Well I would go for A. And let me explain.

From the stem we know that the triangles are similar.
This means that their angles have the same measures and their sides are in proportion.

We are asked to find what percent of the area of triangle DEF triangle ABC is.
To find the area, we need to know the base and the height of a triangle.
What else we know about similar triangles is that the proportion of the area of the triangles is the square of the proportion of their sides. So, if their sides are of a ratio 3:1 their areas would be of a ratio of 9:1.

(1) Sides AB and DE connect similar angles, and AB is 3 times DE.
This statement tells us that 2 angles have the same measure and the leg connecting them is of ratio 3:1. Since we have the ratio, we know that the similar triangles will be of a ratio 3:1. So, their areas will be of a ratio of 9:1.

Now, what I do not understand for sure based on the stem, is what is meant by "triangle ABC". Its area? Its perimenter? I would say that triangle ABC is a triangle of area X and perimenter Y, but I don't know how else I would define a triagle.. I will proceed as if I were looking for the area of ABC and DEF.

Since their areas are of a ratio of 9:1, the ratio of ABC is 9 times that of DEF, and this would give us the percentage. So,  is sufficient.

(2) Side AB = 9. This doesn't tell us anything, as we don't know the relationship between the sides of the triangles. So, we are missing at least the proportion. So, we cannot find the areas. I would say that  is not sufficient.

So....?
Math Expert V
Joined: 02 Sep 2009
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Re: Triangles ABC and DEF are similar. What percent of the area of triangl  [#permalink]

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Bunuel wrote:
Triangles ABC and DEF are similar. What percent of the area of triangle DEF is triangle ABC?

(1) Sides AB and DE connect similar angles, and AB is 3 times DE.
(2) Side AB = 9

Kudos for a correct solution.

VERITAS PREP OFFICIAL SOLUTION:

Solution: A

Start with the easier statement. Statement (2) tells us nothing about the properties of triangle DEF; INSUFFICIENT. Now consider statement (1). If sides AB and DE are similar and side AB is three times side DE, then all three sides and the height of triangle ABC are 3 times their counterparts in triangle DEF. Say the area of ABC is (bh)/2. Since the base and height of triangle DEF are 1/3 of those in ABC, the area of triangle DEF is (1/3b * 1/3h)/2, or (bh/9)/2. Triangle ABC has an area nine times that of triangle DEF, so it is 900% of DEF; SUFFICIENT, (A).
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Triangles ABC and DEF are similar. What percent of the area of triangl  [#permalink]

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Triangles ABC and DEF are similar. What percent of the area of triangle DEF is triangle ABC?

1 Sides AB and DE connect similar angles, and AB is 3 times DE.
2 Side AB = 9
A Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked
B Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked
C Both statements (1) and (2) TOGETHER are sufficient to answer the question asked; but NEITHER statement ALONE is sufficient
D EACH statement ALONE is sufficient to answer the question asked
E Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data specific to the problem are needed
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Math Expert V
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Re: Triangles ABC and DEF are similar. What percent of the area of triangl  [#permalink]

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arvind910619 wrote:
Triangles ABC and DEF are similar. What percent of the area of triangle DEF is triangle ABC?

1 Sides AB and DE connect similar angles, and AB is 3 times DE.
2 Side AB = 9
A Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked
B Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked
C Both statements (1) and (2) TOGETHER are sufficient to answer the question asked; but NEITHER statement ALONE is sufficient
D EACH statement ALONE is sufficient to answer the question asked
E Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data specific to the problem are needed

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Re: Triangles ABC and DEF are similar. What percent of the area of triangl  [#permalink]

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Triangles ABC and DEF are similar. What percent of the area of triangle DEF is triangle ABC?

(1) Sides AB and DE connect similar angles, and AB is 3 times DE

AB = 3 * DE

Area of T. ABC/Area of T. DEF = AB/DE

Area of T. ABC/Area of T. DEF = 1/3

Area of T. ABC = 33% of Area of T. DEF

Hence, =====> (1) is SUFFICIENT

(2) Side AB = 9

We only have information for 1 triangle and we do not know anything about the other triangle.

Hence, =====> (2), is IN SUFFICIENT

Hence, Answer is A
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Re: Triangles ABC and DEF are similar. What percent of the area of triangl  [#permalink]

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(1) makes the two triangles similar and we know that for similar triangles, Area(ABC)/Area(PQR)=AB^2/PQ^2
So sufficient.

(2) doesn't give any information about PQR, or any thing to relate abc to pqr in any way. So insufficient.

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Re: Triangles ABC and DEF are similar. What percent of the area of triangl  [#permalink]

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Referring to Bunuel resources

If two similar triangles have sides in the ratio$$\frac{x}{y}$$, then their areas are in the ratio$$\frac{x^2}{y^2}$$

Statement 1 : AB is 3 times DE and since the both the triangles are similar area will be in ratio$$\frac{3^2}{1^2}$$

=> $$\frac{area ABC}{area DEF} = \frac{9}{1}$$ = 900% Sufficient

Statement 2: No information related to side ration's of triangle, hence insufficient

Ans: A
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Re: Triangles ABC and DEF are similar. What percent of the area of triangl  [#permalink]

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_________________ Re: Triangles ABC and DEF are similar. What percent of the area of triangl   [#permalink] 29 Sep 2018, 06:16
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