To find $x$, the lengths of the two equal sides of the isosceles triangle, we use the Pythagorean theorem. Here's how:

Step-by-step solution:

1. Recognize the geometry of the triangle:

   • The dashed line (height) divides the isosceles triangle into two right triangles.
   • Each of these right triangles has:
     • A base of $\frac{6}{2} = 3$ units.
     • A height of $4$ units.
     • The hypotenuse (one of the equal sides of the isosceles triangle) is $x$.

2. Apply the Pythagorean theorem: For each right triangle: $x^2 = (\text{base})^2 + (\text{height})^2$ Substituting the values: $x^2 = 3^2 + 4^2$

3. Calculate the squares: $x^2 = 9 + 16$ $x^2 = 25$

4. Solve for $x$: $x = \sqrt{25}$ $x = 5$

Final Answer:

$x = 5 \, \text{units.}$

Would you like a detailed geometric explanation or a diagram to accompany this solution?

Related Questions:

1. What are the properties of an isosceles triangle?
2. How do you calculate the area of the triangle using its base and height?
3. What is the perimeter of this triangle?
4. How does the Pythagorean theorem work in other geometric contexts?
5. Can the Pythagorean theorem be used for triangles that are not right triangles?

Tip:

The Pythagorean theorem only applies to right triangles, so look for ways to decompose other triangles into right triangles when solving problems!