Question

Use the Pythagorean Theorem to find X.
A
23
B
25
C
31
D
625

Answer 1

To solve for \( X \) using the Pythagorean theorem, we need to understand the theorem itself. The Pythagorean theorem states that, in a right triangle, the square of the length of the hypotenuse (\( c \)) is equal to the sum of the squares of the lengths of the other two sides (\( a \) and \( b \)). This can be written mathematically as:

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

In this case, I do not have sufficient information about the triangle or what \( X \) represents specifically. If we were to assume that \( A = 23 \), \( B = 25 \), and \( C = 31 \) are the lengths of two sides and the hypotenuse, we can check if any of these values could represent \( c \), the hypotenuse.

1. If \( c = 25 \), we need to check if \( 23 \) and \( x \) can be the other two sides:

\[
25^2 = 23^2 + x^2
\]

Calculating:

\[
625 = 529 + x^2
\]
\[
x^2 = 96
\]
\[
x = \sqrt{96} \approx 9.8
\]

2. If \( c = 31 \) and considering \( A = 23 \):

\[
31^2 = 23^2 + x^2
\]

Calculating:

\[
961 = 529 + x^2
\]
\[
x^2 = 432
\]
\[
x = \sqrt{432} \approx 20.8
\]

3. If \( c = 23 \), then:

\[
23^2 = 25^2 + x^2
\]

This doesn't work because \( 23^2 < 25^2 \).

From this examination, it's clear that \( c \) cannot be lower than either of the other two sides.

Since we haven’t come to a definitive conclusion yet about the possibilities for \( X \) in this context, please clarify what \( X \) is referring to regarding the sides of a triangle or any other information that could help identify \( X \) among the choices. Thank you!