Question

1) Find the value of the variables. Show your work when needed. Write your answer in simplest form.

Answer 1

Given the triangle in the attached image.

We want to find the value of x.

Since the triangle is a right-angled triangle, we can apply the Pythagorean theorem to solve for the variable;

`c^2=a^2+b^2`

For the given triangle;

`\begin{gathered} a=x \\ b=x \\ c=18 \end{gathered}`

substituting the values;

`\begin{gathered} 18^2=x^2+x^2 \\ 18^2=2x^2 \\ x^2=(18^2)/(2) \\ x^2=(324)/(2) \\ x^2=162 \\ x=\sqrt[]{162} \\ x=9\sqrt[]{2} \end{gathered}`

Therefore, the value of the variable x is;