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The problem asks to find the side length \( x \) of a right triangle where the other two sides are 12 and 35 units. This can be solved using the **Pythagorean Theorem**, which states:

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

Where:
- \( a \) and \( b \) are the legs of the right triangle
- \( c \) is the hypotenuse (the longest side opposite the right angle)

From the image:
- \( 12 \) is one leg,
- \( x \) is the other leg,
- \( 35 \) is the hypotenuse.

We apply the Pythagorean theorem:

\[
x^2 + 12^2 = 35^2
\]

First, calculate the squares:
\[
12^2 = 144, \quad 35^2 = 1225
\]

Now substitute:
\[
x^2 + 144 = 1225
\]

Solve for \( x^2 \):
\[
x^2 = 1225 - 144 = 1081
\]

Finally, take the square root:
\[
x = \sqrt{1081} \approx 32.88
\]

So, the side length \( x \) is approximately 32.88 units.

Would you like further details on this solution? 

Here are 5 questions that expand on this topic:
1. What is the Pythagorean theorem used for in geometry?
2. How do you determine which side is the hypotenuse in a right triangle?
3. Can the Pythagorean theorem be used for non-right triangles?
4. What are some real-life applications of the Pythagorean theorem?
5. How would the problem change if the value for the hypotenuse were unknown?

**Tip:** Always ensure you're correctly identifying the hypotenuse before applying the Pythagorean theorem.

For the following right triangle, find the side length x. The triangle has one leg of length 12, another leg of length x, and the hypotenuse of length 35.

Learn how to find the side length x of a right triangle where one leg is 12 units, the hypotenuse is 35 units, and the unknown leg is solved using the Pythagorean theorem. Suitable for students in Grades 7-9.

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