To solve for $x$ in the right triangle, we use the Pythagorean theorem:

$x^2 = a^2 + b^2$

where $a$ and $b$ are the two legs of the right triangle, and $x$ is the hypotenuse.

From the given triangle:

• One leg is $7$,
• The other leg is $2$,
• The hypotenuse is $x$.

Substitute the values into the equation:

$x^2 = 7^2 + 2^2$

$x^2 = 49 + 4$

$x^2 = 53$

Take the square root of both sides:

$x = \sqrt{53}$

Thus, the correct answer is:

A) $x = \sqrt{53}$

Would you like further details or explanations? Here are 5 questions to expand your understanding:

1. How is the Pythagorean theorem applied in non-right triangles?
2. What are some real-world applications of the Pythagorean theorem?
3. Can you determine if a triangle is a right triangle using this theorem?
4. How would the result change if one leg of the triangle was longer than the hypotenuse?
5. What are other methods to find the hypotenuse in right triangles?

Tip: Always verify the triangle's type (right triangle) before applying the Pythagorean theorem.