Question

Finf the value of x and leave your answer in simplest radical form

Answer 1

Divide the shape into smaller triangles

Using pythagoras theorem

`\text{hyp}^2=\text{opp}^2+\text{adj}^2`

For triangle 1

`\begin{gathered} \text{hyp}=y \\ \text{opp}=8 \\ \text{adj}=3 \\ \text{therefore} \\ y^2=8^2+3^2^{} \\ y^2=64+9_{} \\ y^2=73 \\ y=\sqrt[]{73} \end{gathered}`

For triangle 2

`\begin{gathered} \text{hyp}=9 \\ \text{opp}=x \\ \text{adj}=y=\sqrt[]{73} \\ 9^2=x^2+(\sqrt[]{73})^2 \\ 81=x^2+73 \\ x^2=81-73 \\ x^2=8 \\ x=\sqrt[]{8} \\ x=\sqrt[]{4*2} \\ x=2\sqrt[]{2} \end{gathered}`

Hence, the value of x is 2√2