[tex]a = 7\frac{3}{4} \ cm = \frac{31}{4} \ cm\\\\a^{2}+a^{2} = d^{2}\\\\(\frac{31}{4})^{2}+(\frac{31}{4})^{2} = d^{2}\\\\\frac{961}{16}+\frac{961}{16} = d^{2}\\\\d^{2} = \frac{1922}{4}\\\\d = \sqrt{\frac{1922}{16} }= \frac{\sqrt{1922}}{\sqrt{16}}=\frac{\sqrt{961\cdot2}}{4} =\frac{\sqrt{961}\cdot\sqrt{2}}{4} = \frac{31}{4}\sqrt{2}\\\\d = a\sqrt{2} = \frac{31}{4}\sqrt{2} \ cm[/tex]
