This is a right triangle, and since it is also isosceles, the two legs are equal in length. In this case, the hypotenuse is 7, and we need to find the length of the legs $x$. Using the Pythagorean theorem:

$a^2 + b^2 = c^2$

Here, $a = x$, $b = x$, and $c = 7$. Substituting:

$x^2 + x^2 = 7^2$

Simplify:

$2x^2 = 49$

Solve for $x^2$:

$x^2 = \frac{49}{2} = 24.5$

Take the square root of both sides:

$x = \sqrt{24.5}$

$x \approx 4.9$

The length of $x$ to the nearest tenth is 4.9.

Would you like further details or clarification on this solution?

Here are 5 related questions to explore:

1. How does the Pythagorean theorem apply to different types of triangles?
2. What are the properties of isosceles right triangles, and how do they simplify calculations?
3. How do you determine whether a triangle is isosceles given only its side lengths?
4. How is the Pythagorean theorem used in real-world problem solving?
5. What are some common mistakes when solving problems involving right triangles?

Tip: When working with isosceles right triangles, always remember the legs are equal, making it easier to set up the equation for the Pythagorean theorem!