Similar triangles 3-4-5, longest 15

One triangle has sides of 3, 4 and 5 cm. A second triangle is similar to it and its longest side is 15 cm. Find the lengths of the other two sides of the second triangle.

Step-by-step

1. Similarity ratio k = 15 ÷ 5 = 3
   Corresponding sides of similar triangles are proportional (longest to longest)
2. 4 × 3 = 12
   Corresponding sides scale by the same similarity ratio
3. 5 × 3 = 15
   Corresponding sides scale by the same similarity ratio

Why it works

Corresponding sides of similar triangles are in the same ratio, so the longest side of the second triangle divided by the longest side of the first gives the scale factor that applies to the other sides as well.

Common mistakes

• Dividing 15 by the shortest side 3 instead of by 5, which is the side the 15 cm length corresponds to.
• Scaling one side by 3 but leaving the 4 cm side unchanged.

Related

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