To find the length of the hypotenuse of a right triangle, 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.
In this case, one side \( a \) is 17 cm, and the other side \( b \) is 48 cm. Let's calculate the hypotenuse \( c \):
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Calculate \( a^2 \) and \( b^2 \):
\[ a^2 = 17^2 = 289 \] \[ b^2 = 48^2 = 2304 \]
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Add \( a^2 \) and \( b^2 \):
\[ a^2 + b^2 = 289 + 2304 = 2593 \]
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Now take the square root to find \( c \):
\[ c = \sqrt{2593} \]
Thus, the length of the hypotenuse is \(\sqrt{2593}\) cm.
The correct response is:
\[ 2593−−−−√ \text{ cm} \]