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show that of all right triangles inscribed in a circle, the triangle with maximum perimeter is isoceles |
| Answer» RIGHT triangles inscribed in a circleTo FIND : triangle with maximum perimeter is isoscelesSolution: right triangles inscribed in a circleHence hypotenuse will be DIAMETER = c ( constant)Let say one perpendicular side = xthen other perpendicular side = √(c² - x²)Perimeter P = x + √(c² - x²) + c dP/dx = 1 + (-2x)/2√(c² - x²) + 0=> dP/dx = 1 - x/√(c² - x²) dP/dx = 0=> 1 - x/√(c² - x²) = 0=> x/√(c² - x²) = 1=> x = √(c² - x²) => x² = c² - x²=> 2x² = c²=> x² = c²/2=> x = c/√2dP/dx = 1 - x/√(c² - x²) d²P/dx² = 0 - 1/√(c² - x²) - x (-2x)(-1/2)/(c² - x²)√(c² - x²) = - 1/√(c² - x²) - x²/(c² - x²)√(c² - x²) => d²P/dx²< 0Hence P is max for x = c/√2 √(c² - x²) = c/√2Hence sides are c/√2, c/√2 , c=> triangle with maximum perimeter is isoscelesQEDHence provedLearn More:with rectangle of given perimeter finding the one with a maximum ... brainly.in/question/19482093 with rectangle of a given perimeter finding the one with a maximum ... brainly.in/question/3878004 . In about four (4) lines describe how to determine the area and ... brainly.in/question/18731780 | |