



 
Hi Patricia, It is amazing g to me how many times Pythagoras Theorem is what you need to solve everyday problems. I drew a piece of your bathroom wall with the existing hole and labeled three of the vertices. You know that $BC = 12$ inches, $CA = 12$ inches and I let $AB = d$ inches. Pythagoras Theorem says that \[BC^2 + CA^2 = d^2\] so \[12^2 + 12^2 = d^2\] and thus $d^2 = 288$ or $d = 17.0$ inches and hence your 15 inch diameter cover won't work. If the hole is 11.5 inches by 11.5 inches then I get $d^2 = 2 \times 11.5^2$ or $d = 16.3$ inches so that won't work either. I hope this helps,  


Math Central is supported by the University of Regina and the Imperial Oil Foundation. 