# Triangle A has sides of lengths #51 #, #45 #, and #54 #. Triangle B is similar to triangle A and has a side of length #7 #. What are the possible lengths of the other two sides of triangle B?

##### 1 Answer

#### Explanation:

Two similar triangles have all of their side lengths in the same ratio. So, overall there are 3 possible

**Case i) - the 51 length**

So lets have the side length 51 go to 7. This is a scale factor of **all of the sides** by

So the lengths are (as fractions)

**Case ii) - the 45 length**

We do the same thing here. To get the side of 45 to 7, we multiply by

So the lengths are

**Case iii) - the 54 length**

I'm hoping you know what to do by now. We multiply each length by

So the lengths are

All of these triangles, although they have different side lengths, are all similar to triangle A, and all are answers.