Question

I need to figure out the lengths of the triangles.

Answer 1

We need to find the missing lengths for the colored sides of the triangles.

We know that all the triangles are similar.

Thus, each triangle has sides that are proportional to the sides of another triangle.

For the green side, we have:

`\begin{gathered} \frac{\text{ green}}{3}=(12)/(4) \\ \\ \frac{\text{green}}{3}=3 \\ \\ \text{ green }=3\cdot3 \\ \\ \text{ green }=9 \end{gathered}`

For the red side, we have:

`\begin{gathered} \frac{\text{ red}}{4}=(1.5)/(3) \\ \\ \frac{\text{red}}{4}=0.5 \\ \\ \text{ red }=4\cdot0.5 \\ \\ \text{ red }=2 \end{gathered}`

For the orange side, we have:

`\begin{gathered} \frac{\text{ orange}}{3}=(10)/(5) \\ \\ \frac{\text{orange}}{3}=2 \\ \\ \text{ orange }=3\cdot2 \\ \\ \text{ orange }=6 \end{gathered}`

For the blue side, we have:

`\begin{gathered} \frac{\text{ blue}}{4}=(10)/(5) \\ \\ \frac{\text{blue}}{4}=2 \\ \\ \text{ blue }=4\cdot2 \\ \\ \text{blue}=8 \end{gathered}`

Thus, ordering the numbers following the sequence green-red-orange-blue, we obtain:

`9\text{ }2\text{ }6\text{ }8`