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.