Paragraph: Three sides of a trapezium are each equal to 6 cm . Let (0, 2 ) be the angle between a pair of adjacent sides. Question: If the area of the trapezium is the maximum possible, then what is equal to?

Step-by-step solution

Length of three sides of trapezium =6 ~cm Let A E be height of trapezium. aligned & In ADE , AD ^2= AE ^2+ DE ^2 & 6^2= AE ^2+ x ^2 & AE ^2=36- x ^2 & AE = 36- x ^2 aligned Area of trapezium = 1 2 h(a+b) aligned & = 1 2 36-x^2 (6+6+2 x) & A=(6+x) 36-x^2 aligned Given, Area of trapezium is maximum. aligned & d A d x = d d x [(6+x) 36-x^2 ] & =(6+x) ( -2 x 2 36-x^2 )+ 36-x^2 aligned aligned & = 36-x^2 - x(6+x) 36-x^2 & = 36- x ^2-6 x - x ^2 36- x ^2 = 36-6 x -2 x ^2 36-2 x ^2 & dA dx =0 36-6 x -2 x ^2=0 & 2 x ^2+6 x