Question

What is the scale factor here (left is old/right triangle is new)?

Answer 1

The scale factor is 2.

The scale factor must to be the same for all sides of the triangle. if we have the side A and want to know the scale factor to get A', we can write it like an equation:

`A^(\prime)=r\cdot A`

where r is the scale factor, A is the original side length and A' is the new length.

then, if we look at the hypotenuses:

`\begin{gathered} 10=r\cdot5 \\ r=(10)/(5)=2 \end{gathered}`

then the scale factor is 2. to be sure, we can verify this with the other sides

`\begin{gathered} 3\cdot r=3\cdot2=6 \\ 4\cdot r=4\cdot2=8 \end{gathered}`

and all side lengths checks out