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;

$\begin{gathered} 18^2=x^2+x^2 \\ 18^2=2x^2 \\ x^2=\frac{18^2}{2} \\ x^2=\frac{324}{2} \\ x^2=162 \\ x=\sqrt[]{162} \\ x=9\sqrt[]{2} \end{gathered}$

Therefore, the value of the variable x is;