Question

(iii) In the given figure, if AB || CD, find the value of x.

Answer 1

SOLUTION :

(iii) GIVEN : AB || CD ,  OA = (3x – 19),  OB = (x – 4) ,  OC =( x – 3) and OD = 4

Since, the diagonals of a trapezium divide each other proportionally.

Now, AO/OC = BO/OD

(3x–19)/(x–3) = (x–4)/4

4(3x – 19) = (x – 3) (x – 4)

12x – 76 = x(x – 4) -3(x – 4)

12x – 76 = x² – 4x – 3x + 12

12x – 76 = x² – 7x + 12

-x² + 7x – 12 + 12x - 76 = 0

-x² + 7x + 12x – 12 - 76 = 0

-x² + 19x – 88 = 0

x²– 19x + 88 = 0

x² – 11x – 8x + 88 = 0

[By middle term splitting]

x(x – 11) – 8(x – 11) = 0

(x -11) (x - 8) = 0

x = 11 or x = 8

Hence, the value of  x = 11 or x = 8.

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