Similar triangles 3-4-5, shortest 6

One triangle has sides of 3 cm, 4 cm and 5 cm. A second triangle is similar to it and its shortest side is 6 cm. Find the lengths of the other two sides of the second triangle.

Step-by-step

1. Similarity ratio k = 6 ÷ 3 = 2
   Corresponding sides of similar triangles are proportional (shortest to shortest)
2. 4 × 2 = 8
   Corresponding sides scale by the same similarity ratio
3. 5 × 2 = 10
   Corresponding sides scale by the same similarity ratio

Why it works

Corresponding sides of similar triangles are in the same ratio, and the shortest side of one triangle corresponds to the shortest side of the other, so a single scale factor gives the remaining sides.

Common mistakes

• Using 6 ÷ 5 = 1.2 as the scale factor instead of 6 ÷ 3.
• Scaling only one of the two remaining sides.

Related

tangent-line parabola-vertex similar-triangle-3-4-5-longest-15