We are given an isosceles triangle with the following information:

• The two equal sides of the triangle each measure 5 units.
• The base of the triangle has a length of $x$ units.
• The height of the triangle is 6 units.
• A dashed line is drawn from the center of the base to the top vertex, splitting the triangle into two congruent right triangles.

Step-by-step solution:

Since the dashed line splits the triangle into two congruent right triangles, each right triangle will have:

• A height of 6 units.
• Half of the base, which is $\frac{x}{2}$.
• A hypotenuse of 5 units (the equal side of the isosceles triangle).

Now, we apply the Pythagorean theorem to one of these right triangles. According to the Pythagorean theorem, the square of the hypotenuse is equal to the sum of the squares of the two legs:

$\left( \frac{x}{2} \right)^2 + 6^2 = 5^2$

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