The image depicts a right triangle where we are asked to find the hypotenuse, $x$, given the two legs are $4.5$ and $7.5$.

Using the Pythagorean Theorem:

The formula for a right triangle is: $x^2 = a^2 + b^2$ where $a$ and $b$ are the legs, and $x$ is the hypotenuse.

Substituting the values:

$x^2 = 4.5^2 + 7.5^2$ $x^2 = 20.25 + 56.25$ $x^2 = 76.5$ $x = \sqrt{76.5}$

Calculating the square root:

$x \approx 8.74$

Final Answer:

The length of $x$ is approximately 8.74 units.

Would you like further explanations or a different approach?

Related Questions:

1. How is the Pythagorean theorem derived?
2. Can this triangle also be solved using trigonometric functions?
3. How does the accuracy of decimals affect real-world applications of triangle calculations?
4. Can this method be applied to triangles that are not right triangles?
5. What are some practical applications of the Pythagorean theorem?

Tip:

Always ensure the triangle is a right triangle before using the Pythagorean theorem.