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The correct answer is $113$. It's given that the legs of a right triangle have lengths $24$ centimeters and $21$ centimeters. In a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the two legs. It follows that if $h$ represents the length, in centimeters, of the hypotenuse of the right triangle, $h^2={24}^2+{21}^2$. This equation is equivalent to $h^2=\mathrm{1,017}$. Taking the square root of each side of this equation yields $h=\sqrt{\mathrm{1,017}}$. This equation can be rewritten as $h=\sqrt{9·113}$, or $h=\sqrt{9}·\sqrt{113}$. This equation is equivalent to $h=3\sqrt{113}$. It's given that the length of the triangle's hypotenuse, in centimeters, can be written in the form $3\sqrt{d}$. It follows that the value of $d$ is $113$.