To find the length of the hypotenuse in a right triangle with side lengths of 12 inches and 16 inches, we can use the Pythagorean theorem, which states:
\[ c^2 = a^2 + b^2 \]
where \(c\) is the length of the hypotenuse, and \(a\) and \(b\) are the lengths of the other two sides.
Given:
- \(a = 12\) inches
- \(b = 16\) inches
Substituting the values into the theorem:
\[ c^2 = 12^2 + 16^2 \] \[ c^2 = 144 + 256 \] \[ c^2 = 400 \]
Now, take the square root of both sides to find \(c\):
\[ c = \sqrt{400} = 20 \]
Thus, the length of the hypotenuse is \(20\) inches.
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