Similar triangles 6-8-10, shortest 9

One triangle has sides of 6, 8 and 10 cm. A second triangle is similar to it and its shortest side is 9 cm. Find the lengths of the other two sides of the second triangle.

Step-by-step

1. Similarity ratio k = 9 ÷ 6 = 1.5
   Corresponding sides of similar triangles are proportional (shortest to shortest)
2. 8 × 1.5 = 12
   Corresponding sides scale by the same similarity ratio
3. 10 × 1.5 = 15
   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 9 ÷ 10 = 0.9 as the scale factor instead of 9 ÷ 6.
• Adding 3 cm to every side instead of multiplying by the same scale factor.

Related

tangent-line parabola-vertex similar-triangle-5-12-13-shortest-10