Question

What is the value of x?

Enter your answer in the box.

x =
A right triangle. The legs are labeled x and 12, and the hypotenuse is labeled 13.

Answer 1

To find the value of \( x \) in the right triangle, we can use the Pythagorean theorem, which states:

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

where \( c \) is the length of the hypotenuse and \( a \) and \( b \) are the lengths of the legs. In this case, we have:

- One leg \( a = x \)
- The other leg \( b = 12 \)
- The hypotenuse \( c = 13 \)

Substituting these values into the equation gives:

\[
x^2 + 12^2 = 13^2
\]

Calculating \( 12^2 \) and \( 13^2 \):

\[
x^2 + 144 = 169
\]

Now, subtract \( 144 \) from both sides:

\[
x^2 = 169 - 144
\]
\[
x^2 = 25
\]

Next, take the square root of both sides:

\[
x = \sqrt{25}
\]
\[
x = 5
\]

Thus, the value of \( x \) is:

\[
\boxed{5}
\]