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in the given figure ABCD is a trapezoid quadrilateral in quadrilateral AB || DC if OA = 2x+4 cm , OB = 9 x -21 cm , OC = 2x-1 cm and OD= 3 if so x = ?
find value of x

please answer fast it is urgent class 12 th subject maths ​

in the given figure ABCD is a trapezoid quadrilateral in quadrilateral AB DC if OA 2x4 cm OB 9 x 21 cm OC 2x1 cm and OD 3 if so x find value of x please answer class=

Respuesta :

Answer:

x = 1/6 or x = 3

Step-by-step explanation:

Given :

  1. AB ║ DC
  2. OA = (2x + 4) cm
  3. OB = (9x - 21) cm
  4. OC = (2x - 1) cm
  5. OD = 3

Solving :

  • As the sides are parallel, the diagonals are proportional to each other
  • OA/OC = OB/OD
  • (2x + 4)/(2x - 1) = (9x - 21)/3
  • (2x + 4)/(2x - 1) = 3(3x - 7)/3
  • (2x + 4) = (3x - 7)(2x - 1)
  • 2x + 4 = 6x² - 14x - 3x + 7
  • 6x² - 17x - 2x + 3 = 0
  • 6x² - 19x + 3 = 0
  • 6x² - 18x - x + 3 = 0
  • 6x(x - 3) - 1(x - 3) = 0
  • (6x - 1)(x - 3) = 0
  • x = 1/6 or x = 3

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