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06 Feb 2015, 07:33
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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:
25%
(medium)
Question Stats:
71% (01:07) correct
29%
(01:27)
wrong
based on 279
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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.
(1) Sides AB and DE connect similar angles, and AB is 3 times DE.
(2) Side AB = 9
Kudos for a correct solution.
09 Feb 2015, 02:54
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Bookmarks
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, [1] 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 [2] is not sufficient.
So....?
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, [1] 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 [2] is not sufficient.
So....?
09 Feb 2015, 05:57
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Bunuel
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).
