find the area of the largest isosceles triangle whose perimeter is 36cm Share with your friends Share 0 Mayur Pisode answered this Let x, x and y be the sides of an isosceles ∆.Perimeter = 36 cm⇒x + x + y = 36⇒y = 36 - 2xNow, semi - perimeter, s = 18 cmNow, area = ss-xs-xs-y⇒A = 1818-x18-x18-y⇒A2 = 1818-x18-x18-yLet A2=ZNow, Z = 1818-x18-x18-y⇒Z = 1818-x18-x2x-18⇒Z = 36x-182x-9⇒dZdx = 36x-182×1 + x-9×2x-18⇒dZdx = 36x2+324-36x+2x2-36x-18x+324⇒dZdx = 363x2-90x+648⇒dZdx = 108x2- 30x + 216For maxima or minima, dZdx = 0⇒x2- 30x + 216 = 0⇒x2 - 18x - 12x + 216 = 0⇒xx-18-12x-18 = 0⇒x-12x-8 = 0⇒x = 12; 18Now, d2Zdx2 = 1082x-30Now, d2Zdx2x=12 = 10824 - 30 =-648 <0Now, d2Zdx2x=18 = 10836 - 30 =648 >0So, Z is maximum at x = 12So,A2 is maximum at x = 12So, A is maximum at x = 12Maximum area = 1818-1218-122×12-18=18×6×6×6=363 cm2 14 View Full Answer