To use the Pythagorean Theorem, we recall that it states:
\[ a^2 + b^2 = c^2 \]
where \( c \) is the length of the hypotenuse (the longest side) and \( a \) and \( b \) are the lengths of the other two sides of the right triangle.
From the options provided, we can consider two cases.
-
If we are looking for the hypotenuse \( c \):
Given two sides (let's say \( a = 12 \) cm and \( b = 5 \) cm for instance):\[ a^2 + b^2 = c^2 \]
If \( 12 \) and \( 5 \) are example values, that would give:
\[ 12^2 + 5^2 = c^2 \]
\[ 144 + 25 = c^2 \]
\[ 169 = c^2 \]
\[ c = \sqrt{169} = 13 , \text{cm} \] -
If we are looking for one of the shorter sides \( a \) or \( b \):
If the hypotenuse is \( 25 \) cm and one side \( b = 24 \) cm:\[ a^2 + 24^2 = 25^2 \]
\[ a^2 + 576 = 625 \]
\[ a^2 = 625 - 576 \]
\[ a^2 = 49 \]
\[ a = \sqrt{49} = 7 , \text{cm} \]
Given that your response options are \( 169 , \text{cm} \), \( 25 , \text{cm} \), \( 144 , \text{cm} \), and \( 13 , \text{cm} \), we can conclude that the triangle's dimensions we are working with lead us to \( 13 , \text{cm} \) being a valid length when finding a side.
Please provide more context if you want specific sides or checks against particular lengths!