Similarity Math Example 4

Follow the full solution, then compare it with the other examples linked below.

Example 4

medium
Two similar triangles have corresponding side lengths in the ratio 3:53:5. If the perimeter of the smaller triangle is 2727 cm, find the perimeter of the larger triangle.

Solution

  1. 1
    Similar figures scale all linear measurements, including perimeter, by the same factor.
  2. 2
    The scale factor from smaller to larger is 53\frac{5}{3}.
  3. 3
    Multiply the smaller perimeter by the scale factor: 27×53=4527 \times \frac{5}{3} = 45 cm.

Answer

45 cm45 \text{ cm}
For similar shapes, every length changes by the same scale factor. That means perimeter scales exactly the same way as any one corresponding side.

About Similarity

Two figures are similar if they have the same shape but possibly different sizes, meaning all corresponding angles are equal and all corresponding sides are in the same ratio (the scale factor).

Learn more about Similarity →

More Similarity Examples

Example 1 medium

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Example 3 medium

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