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Re: Triangles ABC and DEF are similar. What percent of the area of triangl
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09 Feb 2015, 02:54
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....?