https://file.aiquickdraw.com/mathbot/file/1728716932209emk7nqvd.jpg

The image shows a right triangle with legs measuring 3 inches and 4 inches. We are tasked with finding the length of the hypotenuse \( x \), which is the side opposite the right angle.

To solve for \( x \), we can apply the **Pythagorean Theorem**, which is given by:

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

Where:
- \( a \) and \( b \) are the legs of the triangle,
- \( c \) is the hypotenuse.

In this case:
- \( a = 3 \) inches,
- \( b = 4 \) inches,
- \( c = x \) (the hypotenuse).

Substitute the values into the formula:

\[
3^2 + 4^2 = x^2
\]

\[
9 + 16 = x^2
\]

\[
25 = x^2
\]

Now, take the square root of both sides:

\[
x = \sqrt{25}
\]

\[
x = 5
\]

Thus, the length of \( x \) is **5 inches**.

Would you like more details on the Pythagorean Theorem or have any further questions?

Here are five related questions:
1. What is the Pythagorean Theorem used for in more complex shapes?
2. How would you solve for one leg of the triangle if the hypotenuse and the other leg were known?
3. How does the Pythagorean Theorem relate to distance in coordinate geometry?
4. Can the Pythagorean Theorem be applied in three-dimensional problems?
5. What is the relationship between the Pythagorean Theorem and trigonometry?

**Tip**: Always verify that the triangle is a right triangle before applying the Pythagorean Theorem.

What is the value of x in a right triangle where the legs measure 3 inches and 4 inches?

Learn how to find the hypotenuse of a right triangle with legs measuring 3 inches and 4 inches using the Pythagorean Theorem. This step-by-step guide is perfect for students in Grades 6-8.

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