Mikel is determining if the two triangles below could be similar based on their side lengths.

Triangle R S T. Side R S is 3 centimeters, side S T is 6 centimeters, and side R T is 8 centimeters. Triangle W X U. Side W X is 18 centimeters, side X U is 7.5 centimeters, and side W U is 15 centimeters.

Which statements accurately describe the triangles? Check all that apply.
The common ratio between the triangles is 3 because StartFraction 18 Over 6 EndFraction = 3.
The common ratio between the triangles is 2.5 because StartFraction 7.5 Over 3 EndFraction = 2.5.
The triangles could be similar.
The triangles could not be similar.
The ratios of the side lengths are not consistent.
The ratios of the side lengths are consistent.

For two triangles to be described as similar or congruent, the sides or the angles must be proven to be similar by means of a common ratio. That is, the sides might have different measurements but the ratio by which one side increases or reduces to the match the measurement of the other one must apply to all sides of the triangle consistently.

Considering the triangles in the question, triangle RST has side RS measuring 3 units, while the corresponding side in WXU which is side WX measures 18 units. That means the ratio is 3 : 18 or 1 : 6. This ratio must apply to the other sides of the triangle otherwise they cannot be described as similar. Hence, in triangle RST, if side ST is 6 units, using the ratio of 1 : 6 (or 1/6), then side XU in the other triangle should measure;

1/6 = 6/x

x = 6 *6

x = 36

Since the corresponding side in triangle WXU which is XU measures 7.5 units (and not 36 units), then the ratios of the side lengths are not consistent, and for this reason the triangles could not be similar.