Solution Let the side of the plywood square be \( x \). 1. Construct the square with side length \( x \), let it be ABCD. 2. Draw a perpendicular to \( AC \) at \( C \) and mark point \( E \) on it such that \( CE = x \). 3. By the Pythagorean theorem, note that: \[ AE^2 = AF^2 + CE^2 \]\[ \Rightarrow AE^2 = x^2 + x^2 = 2x^2 \]\[ \Rightarrow AE = \sqrt{2}x. \]4. Similarly, construct a perpendicular to \( AE \) at \( E \) and mark point \( F \) on it such that \( EF = x \). Then, using the Pythagorean theorem again: \[ AF^2 = AE^2 + EF^2 = 2x^2 + x^2 = 3x^2 \]\[ \Rightarrow AF = \sqrt{3}x. \]5. Construct a perpendicular to \( AE \) at \( A \) and mark a point \( G \) such that \( AG = 2x \). 6. This implies that \( AGEF \) is a rectangle. Join \( AG \) and \( FE \). Let they bisect each other at \( X \). 7. \( XFE \) is the required equilateral triangle. 8. \( XFE \) is an equilateral triangle with side length \( x \), this is how: \[ AF = GE \]\[ \Rightarrow XF = XE = \frac{AF}{2} = \frac{2x}{2} = x. \]Also, \( FE = x \). Hence, the construction is complete.