Question

I got stuck and I need help on this I would appreciate the help:0

Answer 1

$x=\frac{9}{\sqrt[]{2}}$

1) In this problem, we can see that this is an isosceles right triangle.

2) So, one way of solving it is to make use of the Pythagorean theorem. Note that an isosceles triangle has two congruent sides, so we can write out:

$\begin{gathered} a^2=b^2+c^2 \\ b=c \\ 9^2=x^2+x^2 \\ 81=2x^2 \\ 2x^2=81 \\ \frac{2x^2}{2}=\frac{81}{2} \\ x^2=\frac{81}{2} \\ \sqrt[]{x^2}=\sqrt[]{\frac{81}{2}} \\ x=\frac{9}{\sqrt[]{2}} \end{gathered}$

Usually, we rationalize it. But since the question requests the denominator to be a rational one, so this is the answer.