Two similar triangles have corresponding sides of 6 cm and 9 cm. If another side of the smaller triangle is 10 cm, find the corresponding side of the larger triangle.

Because the triangles are similar, corresponding side lengths are proportional.

The scale factor from the smaller triangle to the larger triangle is:
9 / 6 = 3 / 2

Let x be the corresponding side of the larger triangle.

Set up the proportion:
x / 10 = 3 / 2

Multiply 10 by 3/2:
x = 10(3/2)
x = 15

Therefore, the corresponding side of the larger triangle is 15 cm.