Multiple choice

Triangle ABC is similar to triangle DEF, where AB corresponds to DE. The perimeter of triangle ABC is 42 centimeters, and the perimeter of triangle DEF is 210 centimeters. The length of AB is 16 centimeters. What is the length of DE?

  1. 5 centimeters

  2. 16 centimeters

  3. 48 centimeters

  4. 80 centimeters
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D Correct answer
Explanation

Ratio of perimeters = ratio of sides. 42 / 210 = 1/5. AB / DE = 1/5. 16 / DE = 1/5. DE = 16 * 5 = 80 cm.

AI explanation

Because triangle ABC is similar to triangle DEF, the ratio of their corresponding sides equals the ratio of their perimeters. The ratio of the perimeter of DEF to the perimeter of ABC is 210 divided by 42, which simplifies to 5. This means DE is 5 times the length of AB. Multiplying the given length of AB, 16 centimeters, by 5 gives the length of DE as 80 centimeters.

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