To find the length of the hypotenuse \( c \) of a right triangle with legs \( a \) and \( b \), we can use the Pythagorean theorem:
\[ c = \sqrt{a^2 + b^2} \]
In this case, both legs \( a \) and \( b \) are 12 cm long. So we can substitute those values into the equation:
\[ c = \sqrt{12^2 + 12^2} \] \[ c = \sqrt{144 + 144} \] \[ c = \sqrt{288} \]
Now, we can simplify \( \sqrt{288} \):
\[ \sqrt{288} = \sqrt{144 \times 2} = \sqrt{144} \times \sqrt{2} = 12\sqrt{2} \]
Next, we will calculate \( 12\sqrt{2} \) using the approximate value of \( \sqrt{2} \approx 1.414 \):
\[ 12\sqrt{2} \approx 12 \times 1.414 = 16.968 \]
Finally, rounding to the nearest hundredth, we get:
\[ 16.968 \approx 16.97 \]
Thus, the length of the hypotenuse is approximately \( \boxed{16.97} \) cm.
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