The image shows a right triangle with one leg measuring 6 units and the other leg measuring 4.5 units. The task is to find the length of the hypotenuse, denoted by $x$.

We can solve this using the Pythagorean theorem, which states:

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

Where $a$ and $b$ are the lengths of the two legs of the triangle, and $c$ is the length of the hypotenuse.

In this case, we have:

• $a = 6$
• $b = 4.5$
• $x = c$

Now applying the Pythagorean theorem:

$6^2 + 4.5^2 = x^2$

$36 + 20.25 = x^2$

$56.25 = x^2$

Taking the square root of both sides:

$x = \sqrt{56.25} = 7.5$

So, the length of the hypotenuse $x$ is 7.5 units.

Would you like further details or have any questions?

Here are some related questions:

1. What is the Pythagorean theorem and when do we apply it?
2. How do you calculate the area of a right triangle?
3. Can we use the Pythagorean theorem for non-right triangles?
4. What is the difference between the hypotenuse and legs in a right triangle?
5. How can we use trigonometry to find the angles of a right triangle?

Tip: In any right triangle, the Pythagorean theorem always holds true, so if you know two sides, you can always find the third.