Multiple choice

The table gives the perimeters of similar triangles ABC and DEF, where AB corresponds to DE. The length of AB is 20 units. Triangle Perimeter Triangle ABC 45 Triangle DEF 360 What is the length of DE, in units?

  1. 8

  2. 16

  3. 160

  4. 180
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C Correct answer
Explanation

For similar triangles, the ratio of perimeters equals the ratio of corresponding sides. P1/P2 = S1/S2. 45/360 = 20/DE. 1/8 = 20/DE. DE = 160.

AI explanation

For similar triangles, the ratio of corresponding sides equals the ratio of their perimeters. The scale factor from triangle ABC to DEF is the perimeter of DEF divided by the perimeter of ABC, which is 360 divided by 45, yielding 8. Multiplying the corresponding side AB of 20 units by this scale factor gives the length of DE as 160 units.

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