Multiple choice

If triangles ABC and DEF are similar such that 2AB = DE and BC = 8 cm, then EF is equal to

  1. 16 cm

  2. 12 cm

  3. 10 cm

  4. 8 cm
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A Correct answer
Explanation

Since triangles ABC and DEF are similar, the ratio of their corresponding sides is constant. Given 2AB = DE, the ratio of sides DE/AB = 2/1. Therefore, the ratio of corresponding sides EF/BC must also be 2/1. With BC = 8 cm, EF = 2 * 8 = 16 cm.

AI explanation

Because triangles ABC and DEF are similar, their corresponding sides are in the same proportion, meaning AB divided by DE equals BC divided by EF. The problem states that 2 times AB equals DE, so the ratio of AB to DE is 1 to 2. Setting up the proportion 1 over 2 equals 8 over EF, we cross multiply to find that EF equals 16 cm.

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