Find the maximum area of a right triangle with hypotenuse 1m.

 

   Find the maximum area of a right triangle with hypotenuse 1m.     

 

   The area of a quadrilater for a given perimeter is maximized when the quadrilateral is a square.     

   So let's assume the same holds true for a triangle, by considering the triangle as half a square.     

 

   If the triangle is half a square, that means both legs are the same length.     

 

   by Pythagoras' Theorem                                          a² + b²  =  c²     

   the legs are equal, which means a = b therefore           2a²  =  1²     

                                                                                            a    =  sqrt(1/2)     and b is the same     

 

   Area of a triangle   =  (1/2) • base • height     

                                 =  (1/2) • sqrt(1/2) • sqrt(1/2)     

                                 =  (1/2) • (1/2)     

                                 =  1/4 meter²     

   _.