Find Missing Side X in Right Triangle ABC: Using Sides 5 and 7 with Pythagorean Theorem

To solve the given problem, we will use the Pythagorean Theorem, which is stated as:

$a^2 + b^2 = c^2$

Here, $c$ represents the hypotenuse, and $a$ and $b$ are the legs of the right triangle. Based on our problem:

• $c = 7$ (the hypotenuse)
• $a = 5$ (one of the legs)
• $b = X$ (the missing side we need to find)

Applying the Pythagorean theorem, we get:

$5^2 + X^2 = 7^2$

Calculating the squares, we have:

$25 + X^2 = 49$

Subtracting 25 from both sides to isolate $X^2$:

$X^2 = 49 - 25$

$X^2 = 24$

Taking the square root of both sides to solve for $X$:

$X = \sqrt{24}$

Therefore, the solution to the problem is $X = \sqrt{24}$, which corresponds to choice 1 in the multiple-choice answers.