A triangle is formed by folding a square card board of side 8 cm at its diagonal. What is the height of the triangle?

4\(\sqrt {2}\) cm

The triangle so formed will be isosceles as BC = DC = 8cm

and third side = diagonal BD = 8\(\sqrt {2}\) cm

DP = half of BD = 4\(\sqrt {2}\)

Height (CP) = \(\sqrt {CD^2 - DP^2}\)

                 = \(\sqrt {8^2 - (4\sqrt {2})^2}\)

                 = \(\sqrt {64 - 32}\)

                 = \(\sqrt {32}\) = 4\(\sqrt {2}\)