To solve the expression \( 38 , \text{units} + 9 , \text{units} = x \):
\[ x = 38 + 9 = 47 , \text{units} \]
Now, regarding the right triangle and the Pythagorean theorem, which states that in a right triangle, the sum of the squares of the lengths of the two shorter sides (legs) is equal to the square of the length of the longest side (hypotenuse):
\[ a^2 + b^2 = c^2 \]
Here, if we assume \( a = 38 , \text{units} \) and \( b = 9 , \text{units} \), we can find \( c \).
Using the values:
\[ a = 38, \quad b = 9 \]
We substitute into the Pythagorean theorem:
\[ 38^2 + 9^2 = c^2 \]
Calculating each square:
\[ 38^2 = 1444 \] \[ 9^2 = 81 \]
Now, add those values together:
\[ 1444 + 81 = 1525 \]
Thus, we have:
\[ c^2 = 1525 \]
Now, to find \( c \), we take the square root:
\[ c = \sqrt{1525} \approx 39.05 , \text{units} \]
So, \( c \approx 39.05 , \text{units} \) is the length of the hypotenuse of the right triangle with sides 38 units and 9 units.