Triangle A has side lengths 3, 4, and 5. Triangle B has side lengths 6,7, and 8.
1. Explain how you know that Triangle B is not similar to Triangle A.
2. Give possible side lengths for Triangle B so that it is similar to Triangle A.
we know that
If two triangles are similar, then the ratio of its corresponding sides is proportional
so
In triangle A
The longest side is 5
the shortes side is 3
In Triangle B
The longest side is 8
the shortes side is 6
Applying proportion
5/8=3/6
5(6)=8(3)
30=24 ------> is not true
That means -----> triangles are not similar
Possible sides lengths for triangle B so that it is similar to Triangle A
Multiply the length sides of triangle A by a scale factor
Assume that the scale factor is 3
so
possible lengths are
3(3)=9
4(3)=12
5(3)=15
triangle B has now length sides 9 , 12 and 15
Verify that the triangle B is similar to triangle A
Apply proportion
3/9=5/15
simplify
1/3=1/3 -----> is true
so
are similar