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You have provided an image of a right triangle, asking to find the length of \(x\). Based on the image, the triangle shows a total horizontal length of 20 feet (14.5 ft + 5.5 ft) and a vertical height of 3.44 feet.

To find \(x\), we can use the Pythagorean theorem, which states:

\[
a^2 + b^2 = c^2
\]

where \(a\) and \(b\) are the legs of the right triangle, and \(c\) is the hypotenuse. Given the measurements:

- One leg \(a = 5.5\) ft (the smaller horizontal segment)
- The other leg \(b = 3.44\) ft (the vertical segment)

Let's calculate \(x\) (the hypotenuse):

\[
x = \sqrt{a^2 + b^2}
\]

Substituting the values:

\[
x = \sqrt{(5.5)^2 + (3.44)^2}
\]

Let's calculate this.The length of \(x\) is approximately \(6.49\) feet.

Would you like any more details or have any other questions? Here are some further topics we could explore:

1. How changing the dimensions of the triangle affects the length of \(x\).
2. Explanation of how the Pythagorean theorem is derived and its historical significance.
3. Similar problems involving right triangles and the use of the Pythagorean theorem.
4. How to check if a triangle is a right triangle given its side lengths.
5. Applying this problem to real-world scenarios, such as construction or navigation.

**Tip:** Always ensure the triangle is a right triangle before applying the Pythagorean theorem, as it only holds true under that condition.

Find the length of x in a right triangle with legs of 5.5 ft (horizontal) and 3.447 ft (vertical).

Learn how to find the length of the hypotenuse in a right triangle using the Pythagorean theorem. Given a horizontal leg of 5.5 feet and a vertical leg of 3.447 feet, apply the formula a^2 + b^2 = c^2 to calculate the hypotenuse. Suitable for students in Grades 8-10.

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