Question

Write an equation that says that the length of the green line is equal to the length of the black line.

Answer 1

The first we need to notice is that the length of the black line is the addition of every segment in which the black line is divided.

So, the total length of the black line is given by:

`L_{\text{black}}=r+r+4r_{}`

Therefore, the length of the black line is:

`L_{\text{black}}=r+r+4r=6r`

Finally, we know that the length of the black segment is equal to that of the green segment, in equation form this looks like:

`L_{\text{green}}=L_{\text{black}}`

And the length of the green segment is equal to 48

`\begin{gathered} L_{\text{green}}=48 \\ \Rightarrow L_{\text{black}}=48 \\ \Rightarrow6r=48 \end{gathered}`

And that's the equation we are looking for

We can go further and solve it