Multiple choice

The perimeters of two similar triangles are 81 cm and 63 cm respectively. If one side of the first triangle be 18 cm, then find the corresponding side of the smaller triangle.

  1. 14 cm

  2. 18 cm

  3. 13 cm

  4. 15 cm
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A Correct answer
Explanation

For similar triangles, the ratio of perimeters is equal to the ratio of corresponding sides. Ratio = 81/63 = 9/7. Let the side of the smaller triangle be x. 18/x = 9/7. x = (18 * 7) / 9 = 2 * 7 = 14 cm.

AI explanation

For similar triangles, the ratio of their corresponding sides is equal to the ratio of their perimeters. We set up the proportion 18 divided by x equals 81 divided by 63. Simplifying the perimeter ratio gives 9 divided by 7, so x equals 18 multiplied by 7 and then divided by 9. Solving this yields a corresponding side length of 14 cm.

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