Question

Find the exact length of the third side. 6 2

Answer 1

We can draw the triangle for clarification:

We can use the pythagoras theorem:

`\begin{gathered} c^2=a^2+b^2 \\ b^2=c^2-a^2 \\ b=\sqrt[]{c^2-a^2}=\sqrt[]{6^2-2^2}=\sqrt[]{36-4} \\ b=\sqrt[]{32}=\sqrt[]{16\cdot2}=\sqrt[]{16}\cdot\sqrt[]{2} \\ b=4\cdot\sqrt[]{2} \end{gathered}`

The exact length of the third side is:

`4\cdot\sqrt[]{2}`