Question

Let a and b be the lengths of the legs of a right triangle

Answer 1

`c=3\sqrt[]{2}`

Step-by-step explanation:

We were given a right triangle having the following properties:

`\begin{gathered} a=3 \\ b=3 \\ c=\text{?} \end{gathered}`

We are to find the length of the unknown side using Pythagoras Theorem:

`\begin{gathered} c^2=a^2+b^2 \\ c^2=3^2+3^2 \\ c^2=9+9 \\ c^2=18 \\ \text{Take the square root of both sides, we have:} \\ c=\sqrt[]{18} \\ c=\sqrt[]{9*2} \\ c=\sqrt[]{9}*\sqrt[]{2} \\ c=3*\sqrt[]{2} \\ c=3\sqrt[]{2} \\ \\ \therefore c=3\sqrt[]{2} \end{gathered}`