To find the length of the base \( x \) of the right-angled triangle using the Pythagorean theorem, we can set up the equation as follows:
\[ c^2 = a^2 + b^2 \]
Where:
- \( c \) is the hypotenuse (9 inches),
- \( a \) is one of the sides (3 inches),
- \( b \) is the other side (which we are trying to find, labeled as \( x \)).
Plugging in the values, we have:
\[ 9^2 = 3^2 + x^2 \]
Calculating the squares:
\[ 81 = 9 + x^2 \]
Subtracting 9 from both sides to isolate \( x^2 \):
\[ 81 - 9 = x^2 \] \[ 72 = x^2 \]
Now, taking the square root of both sides:
\[ x = \sqrt{72} \]
To find the exact value:
\[ \sqrt{72} = \sqrt{36 \cdot 2} = 6\sqrt{2} \]
Calculating \( \sqrt{2} \) (approximately 1.414):
\[ x \approx 6 \cdot 1.414 \approx 8.484 \]
Thus, the approximate length of the wedge of cheese is 8.5 inches.
Therefore, the correct response is:
B 8.5 inches