Question

find the value of $x$.

Short answer

The value of $x$ is $3$.

Step-by-step solution

Step 1. Given information.    

The two sides of triangle are same that is$5$ and third side is$8$.

Step 2. Concept used.

1. In isosceles triangle, the vertex angle bisector of isosceles triangle is perpendicular bisector of the base.
2. Pythagoras Theorem state that in a right angle triangle, the square of the hypotenuse is equal to the sum of squares of other sides.

Step 3. Now find the value.

$\begin{array}{c}BC=CD\left(concept1\right)\\ BD=8\\ BC+CD=8\\ 2BC=8\\ BC=4\end{array}$

Now we can use Pythagoras theorem in $\Delta ABC$.

$\begin{array}{c}{x}^2+8^2=5^2\\ x^2+64=25\\ x^2=9\end{array}$

Taking square root we get.

$\begin{array}{l}x=\pm \sqrt{9}\\ x=\pm 3\end{array}$

Since, distance is always a positive quantity. So we neglect negative sign.

Therefore, the value of x is 3.