Radius of circular hole in triangle

Original area of triangular plate = $\frac{1}{2} \times 88 \times 64 = 2816\text{ cm}^2$.

Area reduced = $\frac{3}{4} \times 2816 = 2112\text{ cm}^2$, which equals the area of the circular hole. $\pi r^2 = 2112$ $\frac{22}{7} r^2 = 2112 \implies r^2 = \frac{2112 \times 7}{22} = 672$ $r = \sqrt{672} = \sqrt{16 \times 42} = 4\sqrt{42}\text{ cm.}$