Question

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 ​

Answer 1

x = 1/6 or x = 3

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