This problem involves a right triangle, so we can use the Pythagorean Theorem to solve for $x$.

The Pythagorean Theorem states that in any right triangle:

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

Where:

• $c$ is the hypotenuse (the longest side, opposite the right angle),
• $a$ and $b$ are the other two sides.

In this case, the 14 unit side is the hypotenuse since it is opposite the right angle of the smaller triangle that forms when you look at the lower right part of the figure.

You can break the original figure into two parts: a rectangle and a right triangle on top. The height of the rectangle is 10, and the base is 5, so the height of the triangle is 4 (14 - 10).

Now, apply the Pythagorean theorem to this triangle, where:

• $a = 4$ (vertical side),
• $b = 5$ (horizontal side),
• $c = x$ (hypotenuse, the slanted side).

$4^2 + 5^2 = x^2$

$16 + 25 = x^2$

$41 = x^2$

Finally, solve for $x$:

$x = \sqrt{41}$

So, the value of $x$ is $\sqrt{41}$.

Do you want further details on any part of this? Let me know if you have any questions!

Here are five related questions to expand your understanding:

1. How do you apply the Pythagorean theorem to a non-right triangle?
2. What happens if you have decimal lengths? How can the theorem be adjusted?
3. How can you find the perimeter of this entire shape?
4. How can you decompose complex shapes into smaller right triangles?
5. How do you simplify radical expressions like $\sqrt{41}$?

Tip: Always check that the triangle you're applying the Pythagorean theorem to is a right triangle.