https://file.aiquickdraw.com/mathbot/file/1729816975710f26cqvus.jpg

The triangle shown in the image is a right triangle. To find the value of \( x \) (the hypotenuse), we can use the **Pythagorean theorem**, which is given by:

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

Here, \( a \) and \( b \) are the legs of the triangle, and \( c \) is the hypotenuse. From the diagram:

- One leg is \( 2 \)
- The other leg is \( 7 \)
- The hypotenuse is \( x \)

Using the Pythagorean theorem:

\[
2^2 + 7^2 = x^2
\]

\[
4 + 49 = x^2
\]

\[
x^2 = 53
\]

\[
x = \sqrt{53}
\]

Thus, the value of \( x \) is \( \sqrt{53} \), which corresponds to option **A**.

Would you like further details on the calculation, or do you have any additional questions?

Here are 5 related questions:
1. How would you find the hypotenuse if the legs were different values?
2. Can the Pythagorean theorem be applied to non-right triangles?
3. What are the common Pythagorean triples?
4. How can you simplify a square root like \( \sqrt{53} \)?
5. How would you find the area of the triangle given in this problem?

**Tip**: The Pythagorean theorem only works for right triangles! Always check that the triangle has a right angle before using it.

Find the value of x in the triangle shown below, where the legs are 2 and 7.

Learn how to use the Pythagorean theorem to find the hypotenuse of a right triangle with legs of lengths 2 and 7. The solution demonstrates step-by-step how to apply the formula a^2 + b^2 = c^2 to calculate the hypotenuse.

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