Multiple choice

The perimeters of (\Delta LMN) and (\Delta XYZ) are 36 cm and 48 cm respectively. (LM = 15) cm. If both are similar triangles, find side XY.

  1. 25

  2. 30

  3. 20

  4. 35
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C Correct answer
Explanation

For similar triangles, the ratio of corresponding sides equals the ratio of perimeters. The ratio of perimeters is 36:48 = 3:4. Since LM corresponds to XY, we have LM/XY = 3/4. Given LM = 15 cm, we get 15/XY = 3/4, which gives XY = 20 cm. This is a direct application of the property that similar triangles have proportional sides and perimeters.

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