Similar triangles 5-12-13, shortest 10

One triangle has sides of 5, 12 and 13 cm. A second triangle is similar to it and its shortest side is 10 cm. Find the lengths of the other two sides of the second triangle.

Step-by-step

1. Similarity ratio k = 10 ÷ 5 = 2
   Corresponding sides of similar triangles are proportional (shortest to shortest)
2. 12 × 2 = 24
   Corresponding sides scale by the same similarity ratio
3. 13 × 2 = 26
   Corresponding sides scale by the same similarity ratio

Why it works

In similar triangles corresponding sides share one scale factor, and the shortest side always corresponds to the shortest side, so that factor converts the other two sides as well.

Common mistakes

• Using 10 ÷ 13 as the scale factor instead of 10 ÷ 5.
• Adding 10 to the other sides instead of multiplying them by the scale factor.

Related

tangent-line parabola-vertex similar-triangle-3-4-5-shortest-6