Question

Use similar triangles to find side lengths. In the diagrams below, A ABC is similar toARST. Use a proportion with sides AB and RS tofind the scale factor of ABC to RST. Use the scale factor from Part I and a proportion to find the length of ST. Use the scale factor from Part I and a proportion to find the length of RT.

Answer 1

When we have similar triangles, we can say that all of the corresponding sides of each of the triangles are in proportion. Then we can say that:

`(AB)/(RS)=(AC)/(RT)=(BC)/(ST)`

Since we have that the measure of sides AB and RS, we can obtain the ratio between these sides - which is, at the same time, the scale factor of triangle ABC to triangle RST:

`\begin{gathered} AB=18 \\ RS=6 \\ (AB)/(RS)=(18)/(6)=3 \end{gathered}`

Therefore, the sides of the triangle ABC are 3 times greater than the sides of the triangle RST.

In summary, therefore, we can say that the scale factor of ∆ABC to ∆RST is 3. In other words, ∆ABC is 3 times greater than ∆RST, or we can say that we need to multiply the sides of ∆RST by 3 to obtain the sides of ∆ABC.

[We can also say that we need to multiply the sides of ∆ABC by 1/3 to obtain the sides of ∆RST.]