Question

Please help to find the value of x and explain how to get it in simple terms.

Answer 1

From the image above

`\begin{gathered} z^2=6^2+3^2\ldots\text{ by pythagora's rule } \\ z^2=36+9 \\ z^2=45 \\ z=\sqrt[]{45} \end{gathered}`

Considering the bigger right angle triangle,

`(3+x)^2=y^2+45`

We can obtain the expression of y from the smaller right angle triangle,

Using pythagora's rule, we have

`y^2=6^2+x^2`

Then, recall

`(3+x)^2=y^2+45`

Substite the expression for y², we have

`(3+x)^2=6^2+x^2+45`

Expand the paranthesis, we have

`\begin{gathered} 9+6x+x^2=x^2+36+45 \\ \text{Subtract x}^2from\text{ both sides } \\ 9+6x=36+45 \\ \end{gathered}`

subtract 9 from both sides, we have

`\begin{gathered} 6x+9-9=81-9 \\ 6x=72 \end{gathered}`

Divide both sides by 6, we obtain

`\begin{gathered} (6x)/(6)=(72)/(6) \\ \text{Then} \\ x=12 \end{gathered}`

Therefore

Answer: x= 12