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Geometry and Trigonometry / Area and volume Difficulty: Easy

Triangle ABC and triangle DEF are similar triangles, where $line segment A B$ and $line segment D E$ are corresponding sides. If $the length of line segment D E equals, 2 times the length of line segment A B$ and the perimeter of triangle ABC is 20, what is the perimeter of triangle DEF ?

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Explanation

Choice B is correct. Since triangles ABC and DEF are similar and $the length of side D E equals, 2 times the length of side A B$ , the length of each side of triangle DEF is two times the length of its corresponding side in triangle ABC. Therefore, the perimeter of triangle DEF is two times the perimeter of triangle ABC. Since the perimeter of triangle ABC is 20, the perimeter of triangle DEF is 40.

Choice A is incorrect. This is half, not two times, the perimeter of triangle ABC. Choice C is incorrect. This is two times the perimeter of triangle DEF rather than two times the perimeter of triangle ABC. Choice D is incorrect. This is six times, not two times, the perimeter of triangle ABC.